I am interested in the mathematical analysis of PDEs which arise in physical applications. I have been particularly interested in problems involving interfaces and phase transitions.
My research is partially supported by NSF DMS-1566578.
with Yuming Zhang, submitted
• Geometry and Stability of normalized mean curvature flow,
with Dohyun Kwon, under revision.
• On Nonlinear Cross-Diffusion systems: an Optimal Transport approach,
with Alpar R. Meszaros, to appear in Cal. Var. and PDE.
• Singular limit of the Porous Medium Equation with a Drift,
with Norbert Pozar and Brent Woodhouse, to appear in Advances in Mathematics.
with Olga Turanova, to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire, 32 pages.
• Liquid Drops on a Rough surface,
with Will Feldman, to appear in Comm. Pure. Appl. Math., 70 pages.
• Congested Aggregation via Newtonian interaction,
with Katy Craig and Yao Yao, Arch. Ration. Mech. Anal. 227 (2018), no. 1, 1 - 67.
• Porous Medium Equation to Hele-Shaw flow with general initial density,
with N. Pozar, Transactions AMS 370 (2018), no.2, 873--909.
• Continuity and Discontinuity of the boundary layer tail,
with W. Feldman, Ann. Sci. Éc. Norm. Supér. 50 (2017), no. 4, 1017--1064.
• A drift approximation for parabolic PDEs with Oblique boundary data ,
with D. Alexander, Transactions of AMS (2016), no.8, 5753-5781.
• Free boundary problems for Tumor Growth: a Viscosity solutions approach,
with B. Perthame and P. Souganidis, Nonlinear Analysis 138 (2016) (a Special Issue on J.L Vazquez's 70th Birthday), 207 - 228.
• Quantitative Homogenization of Elliptic PDEs with Random Oscillatory boundary data,
with W. Feldman and P. Souganidis, J. Math. Pures Appl. (9) 103 (2015), no. 4, 958–1002.
• Quasi-static droplet percolation,
with N. Guillen, Arch. Ration. Mech. Anal. Vol. 215 (2015), no. 1, 211-281.
with S. Choi, Geometric partial differential equations, 105–118, CRM Series, 15, Ed. Norm., Pisa, 2013.
Inwon C. Kim