Publications of YanYan Li


1. pdf typos Degree theory for second order nonlinear elliptic operators and its applications, Comm. in PDE 14 (1989), 1541-1578.

2. pdf Scattering by a potential using hyperbolic methods (with A. Bayliss and C.S. Morawetz), Mathematics of Computation 52 (1989), 321-338.

3. Existence of many positive solutions of semilinear elliptic equations on annulus, J. Differential Equations 83 (1990), 348-367.

4. pdf Nonautonomous nonlinear scalar field equations, Indiana Univ. Math. J. 39 (1990), 283-301.

5. pdf Some existence results of fully nonlinear elliptic equations of Monge-Ampere type, Comm. Pure Appl. Math. 43 (1990), 233-271.

6. pdf Existence of multiple solutions of semilinear elliptic equations in $R^N$, in Variational Methods, Editors, H. Berestycki, J.M. Coron and I. Ekeland, Birkh\"auser, (1990), 133-159.

7. pdf On a min-max procedure for the existence of a positive solution for certain scalar field equations in $R^N$ (with A. Bahri), Revista Matem\'atica Iberoamericana 6 (1990), 1-15.

8. Interior gradient estimates for solutions of certain fully nonlinear elliptic equations, J. of Differential Equations 90 (1991), 172-185.

9. On uniformly rotating stars, Arch. Rat. Mech. Anal. 115 (1991), 367-393.

10. Nonexistence of axially symmetric, stationary solution of Einstein Vacuum Equation with disconnected symmetric event horizon (with G. Tian), Manuscripta Mathematica 73 (1991), 83-89.

11. Existence of infinitely many critical values of some nonsymmetric functionals, J. Differential Equations 95 (1992), 140-153.

12. Existence of solutions for semi-linear elliptic equations with indefinite linear part, J. of Differential Equations 96 (1992), 89-115.

13. Regularity of harmonic maps with prescribed singularities (with G. Tian), Comm. Math. Phys. 149 (1992), 1-30.

14. Continuity of solutions of uniformly elliptic equations in $R^2$ (with S. Chanillo), Manuscripta Mathematica 77 (1992), 415-433.

15. On ``multibump" bound states for certain semilinear elliptic equations (with S. Alama), Indiana Univ. Math. J. 41 (1992), 983-1026.

16. Harmonic maps with prescribed singularities (with G. Tian), Proceeding of Symposia in pure math. (edited by Greene and Yau) 54 (1993), 317-326.

17. pdf On $ -\Delta u = K(x)u^5$ in $R^3$, Comm. Pure Appl. Math. 46 (1993), 303-340.

18. Nonautonomous nonlinear scalar field equations in $R^2$ (with C. Li), J. Differential Equations 103 (1993), 421-436.

19. pdf Prescribing scalar curvature on $S^3$, $S^4$ and related problems, J. Functional Analysis 118 (1993), 43-118.

20. A $\sup + \inf $ inequality for some nonlinear elliptic equations involving exponential nonlinearities (with H. Brezis and I. Shafrir), J. Functional Analysis 115 (1993), 344-358.

21. The Weyl problem with nonnegative Gauss curvature (with P. Guan), J. Diff. Geom. 39 (1994), 331-342.

22. pdf On diameters of uniformly rotating stars (with S. Chanillo), Comm. Math. Phys. 166 (1994), 417-430.

23. pdf Blow up analysis for solutions of $ -\Delta u = Ve^u$ in dimension two (with I. Shafrir), Indiana Univ. Math. J. 43 (1994), 1255-1270.

24. On Nirenberg's problem and related topics, Topological Methods in Nonlinear Analysis 3 (1994), 221-233.

25. pdf On a variational problem with lack of compactness: the topological effect of the critical points at infinity (with A. Bahri and O. Rey), Calculus of Variations and PDEs 3 (1995), 67-93. Also in the preprint series of Centre de Math\'ematiques, Ecole Polytechnique, No. 1017, 1991.

26. pdf Prescribing scalar curvature on $S^n$ and related problems, Part I, J. Diff. Equations 120 (1995), 319-410.

27. Uniqueness theorems through the method of moving spheres (with M. Zhu), Duke Math. J. 80 (1995), 383-417.

28. pdf A note on the Kazdan-Warner type condition (with Z.C. Han), Ann. Inst. Henri Poincare, Analyse nonlin\'eaire, 13 (1996), 283-292.

29. Degenerate elliptic systems and applications to Ginzburg-Landau type equations, Part I (with Z.C. Han), Calculus of Variations and PDEs 4 (1996), 171-202.

30. pdf Prescribing scalar curvature on $S^n$ and related problems, Part II: Existence and compactness, Comm. Pure Appl. Math. 49 (1996), 541-597.

31. The Nirenberg problem in a domain with boundary, Topological Methods in Nonlinear Analysis 6 (1995), 309-329.

32. pdf Monge-Amp\`ere Equations on Riemannian Manifolds (with B. Guan), J. Differential Equations 132 (1996),126-139.

33. Multiple point blow up phenomenon in scalar curvature equations on spheres of dimension greater than three, in Birkhauser, {\it Topics in Geometry}, ed. S. Gindikin, 285-293, 1996.

34. pdf Group invariant convex hypersurfaces with prescribed Gauss-Kronecker curvature, Contemporary Mathematics, AMS, 205 (1997), 203-218.

35. $C^{1,1}$ estimates for solutions of a problem of Alexandrov (with P. Guan), Comm. Pure Appl. Math. 50 (1997), 797-819.

36. Sharp Sobolev trace inequalities on Riemannian manifolds with boundaries (with M. Zhu), Comm. Pure Appl. Math. 50 (1997), 449-487.

37. pdf On a singularly perturbed elliptic equation, Advances in Differential Equations, 2 (1997), 955-980.

38. pdf Sharp Sobolev inequalities involving boundary terms (with M. Zhu), Geometric And Functional Analysis, 8 (1998), 59-87.

39. On a singularly perturbed equation with Neumann boundary condition, Comm. Partial Differential Equations 23 (1998), 487-545.

40. pdf The Dirichlet problem for singularly perturbed elliptic equations (with L. Nirenberg), Comm. Pure Appl. Math. 51 (1998), 1445-1490.

41. pdf Harnack Type Inequality: the Method of Moving Planes, Comm. Math. Phys. 200 (1999), 421-444.

42. pdf Yamabe type equations on three dimensional Riemannian manifolds (with M. Zhu), Communications in Contemporary Math. 1 (1999), 1-50.

43. On the best constant in the Sobolev inequality (with T. Aubin), C.R. Acad. Sci. Paris 328 (1999), 135-138.

44. pdfOn the best Sobolev inequality (with T. Aubin), J. Math. Pures Appl. 78 (1999), 353-387.

45. pdf The Yamabe problem on manifolds with boundaries: Existence and compactness results (with Z.C. Han), Duke Math. J. 99 (1999), 489-542.

46. pdf A priori bounds for co-dimension one isometric embeddings (with G. Weinstein), American Journal of Mathematics 121 (1999), 945-965.

46. pdf: Degree and Sobolev spaces (with H. Brezis, P. Mironescu and L. Nirenberg), Topological Methods in Nonlinear Analysis, 13 (1999), 181-190.

47. Best Sobolev inequalities on Riemannian manifolds (Differential Equations and Mathematical Physics, Proceedings of an International Conference held at the University of Alabama in Birmingham, 1999, 273-278. Editors: R. Weikard and G. Weinstein )

48. The existence of conformal metrics with constant scalar curvature and constant boundary mean curvature (with Z.C. Han), Comm. Anal. Geom. 8 (2000), 809-869.

49. pdf: Gradient estimates for solutions of divergence form elliptic equations with discontinuous coefficients (with M. Vogelius), Arch. Rat. Mech. Anal. 153 (2000), 91-151.

50. Gluing approximate solutions of minimum type on the Nehari manifold (with Z.Q. Wang), USA-Chile Workshop on Nonlinear Analysis, Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 215-223.

51. A note on the scalar curvature problem in the presence of symmetries (with A. Ambrosetti and A. Malchiodi), dedicated to the memory of Ennio De Giorgi, Ricerche di Matematica, Vol. LXIX, 2000, Supplemento, 169-176.

52. ps: A variational result in a domain with boundary (with L. Nirenberg), dedicated to Cathleen Morawetz on the occasion of her 77th birthday, Methods and Applications of Analysis 7 (2000), 489-494.

53. pdf : Fine analysis of blow up and applications, First International Congress of Chinese Mathematicians (Beijing, 1998), 411--421, AMS/IP Stud. Adv. Math., 20, Amer. Math. Soc., Providence, RI, 2001.

54. pdf : Topology and Sobolev spaces (with H. Brezis), J. Functional Analysis 183 (2001), 321-369.

55. pdf : On the Yamabe problem and the scalar curvature problems under boundary conditions (with A. Ambrosetti and A. Malchiodi), Math. Ann. 322 (2002), 667-699.

56. On some conformally invariant fully nonlinear equations (with Aobing Li), C. R. Acad. Sci. Paris, Ser. I 334 (2002), 1-6.

57. pdf Starshaped compact hypersurfaces with prescribed m-th mean curvature in elliptic space (with V. Oliker), Journal of Partial Differential Equations 15 (2002), 68-80.

58. pdf : Some nonlinear elliptic equations from geometry, Proc. Natl. Acad. Sci. USA, Vol. 99, Issue 24, 15287-15290, November 26, 2002.

59. A sharp Sobolev inequality on Riemannian manifolds (with T. Ricciardi), C. R. Acad. Sci. Paris, Ser. I 335 (2002), 519-524.

60. pdf : A sharp Sobolev inequality on Riemannian manifolds (with T. Ricciardi), Communications on Pure and Applied Analysis 2 (2003), 1-31.

61. pdf : An extension to a theorem of J\"orgens, Calabi, and Pogorelov (with L. Caffarelli), Comm. Pure Appl. Math. 56 (2003), 549-583.

62. pdf Estimates for elliptic systems from composite material (with L. Nirenberg), Comm. Pure Appl. Math. 56 (2003), 892-925.

63. dvi On some conformally invariant fully nonlinear equations, Proceedings of the International Congress of Mathematicians, Beijing 2002, vol. 3, 177--184.

64. pdf : Liouville type theorems and Harnack type inequalities for semilinear elliptic equations (with Lei Zhang), Journal d'Analyse Mathematique 90 (2003), 27-87.

65. pdf typos On some conformally invariant fully nonlinear equations (with Aobing Li), Comm. Pure Appl. Math. 56 (2003), 1414-1464.

66. pdf A fully nonlinear version of the Yamabe problem and a Harnack type inequality (with Aobing Li), C. R. Acad. Sci. Paris 336 (2003), 319-324.

67. pdf Some recent work on elliptic systems from composite material, Lectures on Partial Differential Equations, Proceedings in honor of Louis Nirenberg's 75th birthday, New Studies in Advanced Mathematics, Volume 2, Editors: Chang, Lin and Yau, International Press, 2003, 153-158.

68. pdf A Liouville theorem for solutions of the Monge-Amp\`ere equation with periodic data (with L. Caffarelli), Ann. Inst. Henri Poincare, Analyse Nonlineaire 21 (2004), 97-120.

69. dvi Liouville type theorems for some conformally invariant fully nonlinear equations, Rend. Mat. Acc. Lincei, s. 9, v. 14:219-225 (2003) ---- Proceedings of International Conference on Caccioppoli Mathematical Heritage, Academia dei Lincei.

70. pdf A Harnack type inequality for the Yamabe equation in low dimensions (with Lei Zhang), Calculus of Variations and Partial Differential Equations 20 (2004), 133-151.

71. pdf Compactness of solutions to the Yamabe problem (with Lei Zhang), C. R. Acad. Sci. Paris, Ser. I 338 (2004), 693-695.

72. pdf Remark on some conformally invariant integral equations: the method of moving spheres, Journal of the European Mathematical Society 6 (2004), 153-180.

73. pdf The distance function to the boundary, Finsler geometry and the singular set of viscosity solutions of some Hamilton-Jacobi equations (with L. Nirenberg), Comm. Pure Appl. Math. 58 (2005), 85-146.

74. ps A Liouville type theorem for some conformally invariant fully nonlinear equations (with Aobing Li), in Geometric analysis of PDE and several complex variables, 321-328, Contemp. Math. 368, Amer. Math. Soc., Providence, RI, 2005.

75. pdf Generalization of a well known inequality (with L. Nirenberg), in Progress in Nonlinear Differential Equations and Their Applications, Vol. 66, 365-370, 2005, Birkhauser Verlag Basel/Switzerland.

76. pdf Compactness of solutions to the Yamabe problem. II (with Lei Zhang), Calculus of Variations and PDEs 24 (2005), 185-237.

77. pdf On some conformally invariant fully nonlinear equations, Part II: Liouville, Harnack and Yamabe (with Aobing Li), Acta Math. 195 (2005), 117-154

78. pdf Regularity of the distance function to the boundary (with Louis Nirenberg), Rendiconti, Accademia Nazionale delle Scienze detta dei XL, Memorie di Matematica e Applicazioni, 123 (2005), Vol. XXIX, fasc. 1, pagg. 257-264.

79. pdf Starshaped compact hypersurfaces with prescribed k-th Mean Curvature in Hyperbolic Space (with Qinian Jin), Discrete and Continuous Dynamical Systems 15 (2006), 367-377

80. pdf typos A fully nonlinear version of the Yamabe problem on manifolds with boundary (with Aobing Li), J. Eur. Math. Soc. 8 (2006), 295-316.

81. pdf Conformally invariant fully nonlinear elliptic equations and isolated singularities, Journal of Functional Analysis 233 (2006), 380-425.

82. pdf A geometric problem and the Hopf Lemma. I (with Louis Nirenberg), J. Eur. Math. Soc. 8 (2006), 317-339.

83. pdf A geometric problem and the Hopf Lemma. II (with Louis Nirenberg), Chin. Ann. Math. 27B(2), 2006, 193-218.

84. pdf Local gradient estimates of solutions to some conformally invariant fully nonlinear equations, C. R. Acad. Sci. Paris, Ser. I 343 (2006), 249-252.

85. pdf Some multi-valued solutions to Monge-Ampere equations (with L. Caffarelli), Communications in Analysis and Geometry 14 (2006), 411-441.

86. pdf Some nonlinear elliptic equations have only constant solutions (with H. Brezis), J. Partial Differentiaql Equations 19 (2006), 208-217.

87. pdf Nonexistence of positive solutions for some fully nonlinear elliptic equations (with Qinian Jin and Haoyuan Xu), Methods and Applications of Analysis 12 (2005), 441-450.

88. pdf Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary (with Qinian Jin and Aobing Li), Calculus of Variations and PDE's 28 (2007), 509-543.

89. pdf Compactness of solutions to the Yamabe problem. III (with Lei Zhang), Journal of Functional Analysis 245 (2007), 478-474.

90. pdf Degenerate conformally invariant fully nonlinear elliptic equations, Arch. Rational. Mech. and Anal. 186 (2007), 25-51.

91. pdf An extension to a classical theorem of Liouville and applications, in Recent Advances in Nonlinear Partial Differential Equations and Applications, Conference in Honor of the 80th Birthdays of Peter Lax and Louis Nirenberg, June 7-10, 2006, Proceedings of Symposia in Applied Mathematics, American Mathematical Society, page 81-86..

92. pdf Some Liouville theorems and applications, in {\it Perspectives in Nonlinear Partial Differential Equations}, in honor of Haim Brezis, Edited by H. Berestycki, M. Bertsch, F. Browder, L. Nirenberg, L. Peletier and L. Veron, Contemparary Mathematics 446, page 313-317, American Mathematical Society, 2007.

93. pdf Symmetry and Asymmetry: The method of moving spheres (with Qinian Jin and Haoyuan Xu), Advances in Differential Equations 13 (2008), 601-640.

94. pdf Mass and angular-momentum inequalities for axi-symmetric initial data sets. II. Angular-momentum (with P.T. Chrusciel and G. Weinstein), Annals of Physics 323 (2008), 2591-2613.

95. pdf (typos) Results on positive solutions of elliptic equations with a critical Hardy-Sobolev operator (with Daomin Cao), Methods and Application of Analysis 15 (2008), 81-95.

96. pdf Local gradient estimates of solutions to some conformally invariant fully nonlinear equations, Comm. Pure Appl. Math. 62 (2009), 1293-1326.

97. pdf Gradient estimates for the perfect conductivity problem (with Ellen Shiting Bao and Biao Yin), Arch. Rat. Mech. Anal. 193 (2009), 195-226.

98. pdf A Harnack type inequality for some conformally invariant equations on half Euclidean space (with Aobing Li), Acta Mathematica Scientia 29 (2009), 1105-1112.

99. pdf Partial results on extending the Hopf Lemma (with Louis Nirenberg), Rendiconti Di Matematica 29 (2009), 97-115.

100. pdf Some remarks on singular solutions of nonlinear elliptic equations. I. (with Luis Caffarelli and Louis Nirenberg), Journal of Fixed Point Theory and Applications 5 (2009), 353-395.

101. pdf On the local solvability of the Nirenberg problem on $S^2$ (with Zheng-Chao Han), Discrete and Continuous Dynamical Systems 28 (2010), 607-615.

102. pdf Gradient Estimates for the Perfect and Insulated Conductivity Problems with Multiple Inclusions (with Ellen ShiTing Bao and Biao Yin), Comm. in Partial Differential Equations 35 (2010), 1982-2006.

103. pdf Asymptotic behavior of solutions to the $\sigma_k$-Yamabe equation near isolated singularities (with Z.C. Han and E. Teixeira), Invent. Math. 182 (2010), 635-684.

104. pdf A miscellany (with Louis Nirenberg), in ``Percorsi incrociati (in ricordo di Vittorio Cafagna)'', Collana Scientifica di Salerno, Universit\`a Degli Studi Di Salerno ------- Cross paths (in memory of Vittorio Cafagna), Academic Scientific Series, University of Salerno, 2010, 193-208 ; see also arXiv:math.AP/0910.0323v1 2 Oct 2009, 16 pages.

105. pdf Remarks on mean value properties (with Luc Nguyen), Progress in variational methods, 52-70, Nankai Ser. Pure Appl. Math. Theoret. Phys., 7, World Sci. Publ., Hackensack, NJ, 2011.

106. pdf A Nonlinear Elliptic PDE with Two Sobolev-Hardy Critical Exponents (with C.S. Lin), Arch. Rat. Mech. Anal. 203 (2012), 943-968.

107. pdf The work of Louis Nirenberg, Proceedings of the International Congress of Mathematicians, Volume I, 127-137, Hindustan Book Agency, New Delhi, 2010.

108. pdf On fully nonlinear CR invariant equations on the Heisenberg group (with Dario Daniele Monticelli), Journal Differential Equations 252 (2012), 1309-1349.

109. pdf A geometric characterization of a sharp Hardy inequality (with Roger T. Lewis and Junfang Li), Journal of Functional Analysis 262 (2012), 3159-3185.

110. pdf Hypersurfaces of Prescribed Curvature Measure (with Pengfei Guan and Junfang Li), Duke Math. J. 161 (2012), 1927-1942.

111. pdf Counterexamples to $C^2$ boundary estimates for a fully nonlinear Yamabe problem on manifolds with boundary (with Luc Nguyen), Advanced nonlinear Studies 12 (2012), 783-797.

112. pdf On conformally invariant equations on R^n -- II. Exponential invariance, (with Paolo Mastrolia and Dario Daniele Monticelli), Nonlinear Analysis: Theory, Methods & Applications 75 (2012), 5194-5211.

113. pdf Some remarks on singular solutions of nonlinear elliptic equations. II: symmetry and monotonicity via moving planes (with Luis Caffarelli and Louis Nirenberg), in Advances in Geometric Analysis, edited by Stanislaw Janeczko, Jun Li and Duong H. Phong, International Press, 2012, 97-105.

114. pdf The Calabi-Yau equation on $4-$manifolds over $2-$tori (with A. Fino, S. Salamon and L. Vezzoni), Transaction of the American Mathematical Society 365 (2013), 1551-1575.

115. pdf Some remarks on singular solutions of nonlinear elliptic equations. III: viscosity solutions, including parabolic operators (with Luis Caffarelli and Louis Nirenberg), Comm. Pure Appl. Math. 66 (2013), 109-143.

116. pdf A generalized mass involving higher order symmetric function of the curvature tensor (with Luc Nguyen), Ann. Henri Poincare 14 (2013), 1733-1746.

117. pdf On conformally invariant equations on R^n, (with Paolo Mastrolia and Dario Daniele Monticelli), Nonlinear Analysis: Theory, Methods & Applications 95 (2014), 339-361.

118. pdf A fully nonlinear version of the Yamabe problem on locally conformally flat manifolds with umbilic boundary (with Luc Nguyen), Adv. Math. 251 (2014), 87-110.

119. pdf A compactness theorem for a fully nonlinear Yamabe problem under a lower Ricci curvature bound (with Luc Nguyen), Journal of Functional Analysis 266 (2014), 3741-3771.

120. pdf On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions (with Tianling Jin and Jingang Xiong), J. Eur. Math. Soc. (JEMS) 16 (2014), 1111-1171.

121. pdf Derivative estimates of solutions of elliptic systems in narrow domains (with HaiGang Li, Ellen ShiTing Bao and Bian Yin), Quarterly of Applied Mathematics 72 (2014), 589-596.

122. pdf Harnack inequalities and Bocher-type theorems for conformally invariant fully nonlinear degenerate elliptic equations (with Luc Nguyen), Comm. Pure Appl. Math. 67 (2014), 1843-1876.

123. pdf On the exterior Dirichlet problem for Hessian equations (with Jiguang Bao and Haigang Li), Trans. Amer. Math. Soc. 366 (2014), 6183-6200.

124. pdf Gradient estimates for solutions of the Lame system with partially infinite coefficients (with JiGuang Bao and HaiGang Li, Arch. Rat. Mech. Anal. 215 (2015), 307-351.

125. pdf On a fractional Nirenberg problem, part II: existence of solutions (with Tianling Jin and Jingang Xiong), International Mathematics Research Notices 2015, no. 6, 1555-1589.

126. pdf On the C^1 regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients, Chin. Ann. Math. Ser. B 38 (2017), no. 2, 489-496.

127. pdf A degree theory for second order nonlinear elliptic operators with nonlinear oblique boundary conditions (with Jiakun Liu and Luc Nguyen), Journal of Fixed Point Theory and Applications 19 (2017), 853-876.

128. pdf Gradient estimates for solutions of the Lame system with partially infinite coefficients in dimensions greater than two (with JiGuang Bao and HaiGang Li), Adv. Math. 305 (2017), 298-338.

129. pdf Symmetry, quantitative Liouville theorems and analysis of large solutions of conformally invariant fully nonlinear elliptic equations (with Luc Nguyen), Calc. Var. Partial Differential Equations 56 (2017), no. 4, Art. 99, 35 pp.

130. pdf The Nirenberg problem and its generalizations: A unified approach (with Tianling Jin and Jingang Xiong), Math. Ann. 369 (2017), 109-151.