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vogelius@math.rutgers.edu

Last updated: 7/18/98



Publications


 
Below is a chronological list of my published papers.
  1. On mathematical modelling - dimensional reduction. In Proceedings of the Finite Element Workshop (Ed. I. Babuska), College Park, May 1980, pp. 58-76.

  2. On a dimension reducing technique - applications to water waves. In Advances in Computer Methods for Partial Differential Equations IV. (Ed. R. Vichnevetsky and R. Stepleman) IMACS (1981), pp. 23-27.

  3. On a dimensional reduction method. The optimal selection of basis functions. Math. Comp., 37 (1981), pp. 31-46. (with I. Babuska).

  4. On a dimensional reduction method. Some approximation-theoretic results. Math. Comp., 37 (1981), pp. 47-68. (with I. Babuska).

  5. On a dimensional reduction method. A-posteriori error estimation and an adaptive approach. Math. Comp., 37 (1981), pp. 361-384.(with I. Babuska).

  6. A variational method to find effective coefficients for periodic media. A comparison with standard homogenization. In Macroscopic Properties of Disordered Media (Eds. R. Burridge, S. Childress and G. Papanicolaou). Lecture Notes in Physics 154, Springer Verlag (1982), pp. 285--296.

  7. A projection method applied to diffusion in a periodic structure. SIAM J. Appl. Math., 42 (1982), pp. 1302-1322. (with G. Papanicolaou).

  8. Adaptive methods and error estimation for elliptic problems of structural mechanics. In Adaptive Computational Methods for Partial Differential Equations (Eds. I. Babuska, J. Chandra and J.E. Flaherty) SIAM (1983), pp. 57-73. (with I. Babuska and A. Miller).

  9. A right inverse for the divergence operator in spaces of piecewise polynomials. Application to the p-version of the Finite Element Method. Num. Math., 41 (1983), pp. 19-37.

  10. An analysis of the p-version of the Finite Element Method for nearly incompressible materials. Uniformly valid optimal error estimates. Num. Math., 41 (1983), pp. 39-53.

  11. Identification of an unknown conductivity by means of measurements at the boundary. In Inverse Problems (Ed. D.W. McLaughlin) SIAM-AMS Proceedings, 14 (1984), pp. 113-123. (with R. Kohn).

  12. A new model for thin plates with rapidly varying thickness. Int. J. of Solids and Structures, 20 (1984), pp. 333-350. (with R. Kohn).

  13. Determining conductivity by boundary measurements. Comm. Pure and Applied Math., 37 (1984), pp. 289-298. (with R. Kohn).

  14. Feedback and adaptive finite element solution of one-dimensional boundary value problems. Num. Math., 44 (1984), pp. 75-102. (with I. Babuska).

  15. Conforming finite element methods for incompressible and nearly incompressible continua. Lect. Appl. Math., vol 22 (Eds. B. Engquist, S. Osher and R. Sommerville) AMS (1985), pp. 221-243. (with L.R. Scott).

  16. A new model for thin plates with rapidly varying thickness II: A convergence proof. Quarterly of Applied Math., 43 (1985), pp. 1-22. (with R. Kohn).

  17. Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials. Math. Modelling Num. Anal. (R.A.I.R.O.), 19 (1985), pp. 111-143. (with L.R. Scott).

  18. Determining conductivity by boundary measurements II. Interior results. Comm. Pure and Applied Math., 38 (1985), pp. 643-667. (with R. Kohn).

  19. Thin plates with rapidly varying thickness and their relation to structural optimization. In proceedings of the Minnesota Institute Workshop on Homogenization and Effective Moduli of Materials and Media, IMA Volumes in Mathematics and its Applications 1 (Eds. J. Ericksen, D. Kinderlehrer, R. Kohn and J.L. Lions) Springer Verlag (1986), pp. 126-149. (with R. Kohn).

  20. A new model for thin plates with rapidly varying thickness III: Comparison of different scalings. Quarterly of Applied Math., 44 (1986),pp. 35-48. (with R. Kohn).

  21. Relaxation of a compliance functional for a plate optimization problem. In Proceedings of the International Conference on the Applications of Multiple Scaling in Mechanics (Eds. P. Ciarlet and E. Sanchez Palencia) Masson (1987), pp. 31-53. (with E. Bonnetier).

  22. Homogenization limits of the equations of elasticity in thin domains. SIAM J. Math. Anal., 18 (1987), pp. 435-451. (with A. Damlamian).

  23. Relaxation of a variational method for impedance computed tomography. Comm. Pure and Applied Math., 40 (1987), pp. 745-777. (with R. Kohn).

  24. Homogenization limits of diffusion equations in thin domains. Math. Modelling Num. Anal., 22 (1988), pp. 53-74. (with A. Damlamian)

  25. Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Annali Scuola Norm. Sup. Pisa, Serie 4, 15 (1988), pp. 169-192. (with D.N. Arnold and L.R. Scott).

  26. Identification of objects of extreme conductivity by boundary measurements. In Control and Estimation of Distributed Parameter Systems (Eds. F.Kappel, K.Kunisch and W. Schappacher) Int. Ser. Num. Math., vol. 91, Birkhauser Verlag (1989), pp. 135-144. (with A. Friedman).

  27. Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependence. Arch. Rational Mech. Anal., 105 (1989), pp. 299-326. (with A. Friedman).

  28. Determining cracks by boundary measurements. Indiana Univ. Math. J., 38 (1989), pp. 527-556. (with A. Friedman).

  29. A computational method for electrical impedance imaging. In Control of Distributed Parameter Systems (Eds. M. Amouroux and A. El-Jai) IFAC Symposia Series, no. 3, Pergamon Press (1990), pp. 187-192 . (with F. Santosa).

  30. A backprojection algorithm for electrical impedance imaging. SIAM J. Appl. Math., 50 (1990), pp. 216-243. (with F. Santosa).

  31. Divergence stability in connection with the p-version of the Finite Element Method. Math. Modelling Num. Anal., 24 (1990), pp. 737-764. (with S. Jensen).

  32. A homogenization result for planar, polygonal networks. Math. Modelling Num. Anal., 25 (1991), pp. 483-514.

  33. An inverse problem originating from magnetohydrodynamics. Arch. Rational Mech. Anal., 115 (1991), pp. 137-152. (with E. Beretta).

  34. A computational algorithm to determine cracks from electrostatic boundary measurements. Int. J. Engng. Sci., 29 (1991), pp. 917-937. (with F. Santosa).

  35. An inverse problem originating from magnetohydrodynamics. Some numerical experiments. In Ill-posed Problems in Natural Sciences (Ed. A.N. Tikhonov) VSP, Utrecht (1992), pp. 254-269. (with E. Beretta and E. Fischer).

  36. A uniqueness result concerning the identification of a collection of cracks from finitely many electrostatic boundary measurements. SIAM J. Math. Anal., 23 (1992), pp. 950-958. (with K. Bryan).

  37. An inverse problem originating from magnetohydrodynamics II. The case of the Grad-Shafranov equation. Indiana Univ. Math. J., 41 (1992), pp. 1081-1118. (with E. Beretta).

  38. First order corrections to the homogenized eigenvalues of a periodic composite medium. SIAM J. Appl. Math., 53 (1993), pp. 1636-1668. (with F. Santosa). Erratum to same: 55 (1995), p. 864.

  39. Crack determination from boundary measurements - Reconstruction using experimental data. J. Nondestructive Evaluation, 12 (1993), pp. 163-174. (with V. Liepa and F. Santosa).

  40. Reconstruction of multiple cracks from experimental, electrostatic boundary measurements. In Inverse Problems and Optimal Design in Industry (Eds. H.W. Engl and J. McLaughlin) Teubner, Stuttgart (1994), pp. 147-167. (with K. Bryan and V. Liepa).

  41. A computational algorithm to determine crack locations from electrostatic boundary measurements. The case of multiple cracks. Int. J. Engng. Sci., 32 (1994), pp. 579-603. (with K. Bryan).

  42. An inverse problem for the equation Delta u=-cu-d. Annales de l'Institut Fourier, 44 (1994), pp. 1181-1209.

  43. A note concerning boundary effects and the long time vibrations of layered media. IMA Volumes in Mathematics and its Applications 70 (Eds. J.E. Lagnese, D.L. Russell, and L.W. White) Springer Verlag (1994), pp. 213-228. (with F. Santosa).

  44. An inverse problem originating from magnetohydrodynamics III. Domains with corners of arbitrary angles. Asymptotic Analysis, 11 (1995), pp. 289-315. (with E. Beretta).

  45. A method for imaging corrosion damage in thin plates from electrostatic data. Inverse Problems, 12 (1996), pp. 279-293. (with P. Kaup and F. Santosa).

  46. First order corrections to the homogenized eigenvalues of a periodic composite medium. A convergence proof. Proc. Roy. Soc. Edinburgh, 127A (1997), pp. 1263-1299. (with S. Moskow).

  47. Effective behaviour of clusters of microscopic cracks inside a homogeneous conductor. Asymptotic Analysis, 16 (1998), pp. 141-179. (with K. Bryan).

  48. Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction. Inverse Problems, 14 (1998), pp. 553-595. (with D.J. Cedio-Fengya and S. Moskow).

  49. A nonlinear elliptic boundary value problem related to corrosion modeling. Quarterly of Applied Math., 56 (1998), pp. 479-505. (with J.-M. Xu).

  50. An effective nonlinear boundary condition for a corroding surface. Identification of the damage based on steady state electric data. Zeitschrift fuer Angewandte Mathematik und Physik, 49 (1998), pp. 656-679. (with F. Santosa and J.-M. Xu).

  51. Determination of the interface between the fluids in a Hall-Heroult cell from measurements of electric potentials and currents on the electrodes. SIAM J. Control and Optimization, 37 (1999), pp. 245-277. (with D.J. Cedio-Fengya and M.V. Romerio).

  52. An elliptic regularity result for a composite medium with "touching" fibers of circular cross-section. SIAM J. Math. Anal., 31 (2000), pp. 651--677. (with E. Bonnetier).

  53. Gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients. Arch. Rational Mech. and Anal., 153 (2000), pp. 91--151. (with Y.-Y. Li).

  54. Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter. Modelisation Mathematique et Analyse Numerique, 34 (2000), pp. 723--748. (with D. Volkov).

  55. Asymptotic formulas for steady state voltage potentials in the presence of conductivity imperfections of small area. Zeitschrift fuer Angewandte Mathematik und Physik, 52 (2001), pp. 543--572. (with E. Beretta and A. Mukherjee).

  56. Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter II. The full Maxwell Equations. Journal Mathematiques Pures et Appliquees, 80 (2001), pp. 769--814. (with H. Ammari and D. Volkov).

  57. Singular solutions to a nonlinear elliptic boundary value problem originating from corrosion modeling. Quarterly of Applied Math., 60 (2002), pp. 675--694. (with K. Bryan).

  58. Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume. ESAIM: Cont. Opt. Calc. Var., 9 (2003), pp. 49--66. (with H. Ammari and S. Moskow).

  59. A direct impedance tomography algorithm for locating small inhomogeneities. Numerische Mathematik, 93 (2003), pp. 635--654. (with M. Bruehl and M. Hanke).

  60. On the existence and "blow-up" of solutions to a two dimensional nonlinear boundary value problem arising in corrosion modeling. Proc. Roy. Soc. Edinburgh, 133A (2003), pp. 119--149. (with O. Kavian). Corrigendum to same: 133A (2003), pp. 729--730.

  61. A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction. Math. Modelling Num. Anal., 37 (2003), pp. 159--173. (with Y. Capdeboscq).

  62. Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements. Math. Modelling Num. Anal., 37 (2003), pp. 227--240. (with Y. Capdeboscq).

  63. Asymptotic formulas for steady state voltage potentials in the presence of thin inhomogeneities. A rigorous error analysis. Journal Mathematiques Pures et Appliquees, 82 (2003), pp. 1277--1301. (with E. Beretta and E. Francini).

  64. A review of selected works on crack identification. IMA Volumes in Mathematics and its Applications 137 (Eds. C. Croke, I. Lasiecka, G. Uhlmann and M.S. Vogelius) Springer Verlag (2004), pp. 25--46. (with K. Bryan).

  65. A review of some recent work on impedance imaging for inhomogeneities of low volume fraction. Contemporary Mathematics 362 (Eds. C. Conca, R. Manasevich, G. Uhlmann, and M.S. Vogelius) AMS (2004), pp. 69--88. (with Y. Capdeboscq).

  66. Blow up behaviour of planar harmonic functions satisfying a certain exponential Neumann boundary condition. SIAM J. Math. Anal., 36 (2005), pp. 1772--1806. (with K. Medville).

  67. Existence and blow up of solutions to certain classes of two dimensional nonlinear Neumann problems. Annales de l'Institut Henri Poincare Analyse Non Lineaire, 23 (2006), pp. 499--538. (with K. Medville).

  68. Pointwise polarization tensor bounds, and applications to voltage perturbations caused by thin inhomogeneities. Asymptotic Analysis, 50 (2006), pp. 175--204. (with Y. Capdeboscq).

  69. Asymptotically precise norm estimates of scattering from a small circular inhomogeneity. Applicable Analysis, 86 (2007), pp. 433--458. (with D.J. Hansen and C. Poignard).

  70. Imagerie electromagnetique de petites inhomogeneites. ESAIM: Proceedings, 22 (Eds. G. Caloz and M. Dauge) EDP Sciences, SMAI (2007), pp. 40--51. (with Y. Capdeboscq).

  71. A MUSIC-type algorithm for detecting internal corrosion from electrostatic boundary measurements. Numerische Mathematik, 108 (2008), pp. 501-528. (with H. Ammari, H. Kang, E. Kim and K. Louati).

  72. Cloaking via change of variables in Electrical Impedance Tomography. Inverse Problems, 24 (2008), 015016, 21pp. (with R.V. Kohn, H. Shen and M.I. Weinstein).

  73. High frequency perturbation formulas for the effect of small inhomogeneities. Proceedings of 6th ICIPE. Journal of Physics: Conference Series, 135 (Eds. M. Bonnet et. al.} IOP Publishing (2008), 012106, 27pp. (with D.J. Hansen).

  74. A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity. Annales de l'Institut Henri Poincare / Analyse Non Lineaire, 26 (2009), pp. 2283--2315. (with H.M. Nguyen).

  75. Cloaking via change of variables for the Helmholtz Equation. Comm. Pure & Applied Math., 63 (2010), pp. 973--1016. (with R.V. Kohn, D. Onofrei and M.I. Weinstein).

  76. Precise bounds for finite time blow-up of solutions to very general one space-dimensional nonlinear Neumann problems. Quarterly of Applied Math., 69 (2011), pp. 57-78. (with K. Bryan).

  77. Transient behavior of solutions to a class of nonlinear boundary value problems. Quarterly of Applied Math., 69 (2011), pp. 261-290. (with K. Bryan).

  78. Full range scattering estimates and their application to cloaking. Arch. Rat. Mech. Anal., 203 (2012), pp. 769--807. (with H.M. Nguyen).

  79. Approximate cloaking for the full wave equation via change of variables. SIAM J. Math Anal., 44 (2012), pp. 1894--1924. (with H.M. Nguyen).

  80. Diffusion and homogenization limits with separate scales. SIAM Multiscale Modeling and Simulation, 10 (2012), pp. 1148--1179. (with N. Ben Abdallah and M. Puel).

  81. Analysis of an enhanced approximate cloaking scheme for the conductivity problem. Asymptotic Analysis, 87 (2014), pp. 223--246. (with H. Heumann).

  82. Elliptic estimates in composite media with smooth inclusions: an integral equation approach. Annales scientifiques de l'Ecole normale superieure, 47 (2014), 50 pp. (with H. Ammari, E. Bonnetier, and F. Triki).

  83. Enhanced approximate cloaking by optimal change of variables. Inverse Problems, 30 (2014), 035014, 17pp. (with R. Griesmaier).



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