Dennis Kriventsov

Rutgers University
Hill Center 524
110 Frelinghuysen Road
Piscataway, NJ 08854-8019
dennis.kriventsov at rutgers.edu

I am an assistant professor in the mathematics department. Here is my CV.

Teaching

Spring 2025: Elementary Differential Equations (252), Partial Differential Equations 2 (518).

For past semesters see here.

Office Hours: MW 16:00 in Hill 524, or by appointment

Research

I study regularity of elliptic and parabolic equations, especially with nonlocal aspects, as well as some free boundary problems.

My research is partially supported by NSF DMS grant 2247096.

If you are a student interested in doing math research with me, see here.

Publications

• Allen, M., Kriventsov, D., and Shahgholian, H. The free boundary for semilinear problems with highly oscillating singular terms. Preprint (2024) arXiv
• Kriventsov, D., and Soria-Carro, M. A parabolic free transmission problem: flat free boundaries are smooth. Preprint (2024) arXiv
• Kriventsov, D., and Li, Z. Asymptotic expansions for harmonic functions at conical boundary points. Rev. Mat. Iberoam. To appear (2025) arXiv paper
• Kriventsov, D., and Weiss, G. Rectifiability, finite Hausdorff measure, and compactness for non-minimizing Bernoulli free boundaries. Comm. Pure Appl. Math. 78, issue 3 (2025) arXiv paper
• Allen, M., Kriventsov, D., and Neumayer, R. Rectifiability and uniqueness of blow-ups for points with positive Alt-Caffarelli-Friedman limit. Math. Ann. (2025) arXivpaper
• Allen, M., Kriventsov, D., and Neumayer, R. Sharp quantitative Faber-Krahn inequalities and the Alt-Caffarelli-Friedman monotonicity formula. Ars Inven. Anal. Paper 1 (2023) arXiv paper
• Allen, M., Kriventsov, D., and Neumayer, R. Linear Stability Implies Nonlinear Stability for Faber-Krahn Type Inequalities. Interfaces Free Bound. 25, issue 2 (2023) arXiv paper
• Allen, M., Kriventsov, D., and Shahgholian, H. The Inhomogeneous Boundary Harnack Principle for Fully Nonlinear and p-Laplace equations. Ann. Inst. H. Poincare C Anal. Non Lineaire 40, issue 1 (2022) arXiv paper
• Jin, T., Kriventsov, D., and Xiong, J. On a Rayleigh-Faber-Krahn inequality for the regional fractional Laplacian. Ann. Appl. Math. 37, issue 3 (2021) arXiv paper
• Kriventsov, D., and Shahgholian, H. Optimal regularity for a two-phase obstacle-like problem with logarithmic singularity. To appear, Comm. in PDE. (2021) arXiv paper
• Allen, M. and Kriventsov, D. A spiral interface with positive Alt-Caffarelli-Friedman limit at the origin. Analysis & PDE 22, issue 1 (2020) arXiv paper
• Kriventsov, D. and Lin, F. Regularity for Shape Optimizers: The Degenerate Case. Comm. Pure Appl. Math. 72, issue 8 (2019) arXiv paper
• Kriventsov, D. and Lin, F. Regularity for Shape Optimizers: The Nondegenerate Case. To appear, Comm. Pure Appl. Math. 71, issue 8 (2018) arXiv paper
• Kriventsov, D. A Free Boundary Problem Related to Thermal Insulation: Flat Implies Smooth. Calc. Var. Partial Diff. 58, issue 2 (2019) arXiv paper
• Chang-Lara, H. and Kriventsov, D. Further Time Regularity for Non-Local, Fully Non-Linear Parabolic Equations. Comm. Pure Appl. Math. 70, issue 5 (2017) arXiv paper
• Caffarelli, L. A. and Kriventsov, D. A Free Boundary Problem Related to Thermal Insulation. Comm. in PDE. 41, issue 7 (2016) arXiv paper
• Chang-Lara, H. and Kriventsov, D. Further time regularity for fully non-linear parabolic equations. Math. Res. Lett. 22, issue 6 (2015) arXiv paper
• Kriventsov, D. Regularity for a Local-Nonlocal Transmission Problem. Arch. Rat. Mech. Anal. 237, issue 3 (2015) arXiv paper
• For those interested in transmission problems, you may want to look at my thesis, which treats more example and has some further discussion.
• Kriventsov, D. C^{1,\alpha} Interior Regularity for Nonlinear Nonlocal Elliptic Equations With Rough Kernels. Comm. in PDE. 38, issue 12 (2013) arXiv paper