Papers & Preprints
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 analysis program DMS-1566578.
with Yuming Zhang.
with Norbert Pozar and Brent Woodhouse.
• On Nonlinear Cross-Diffusion systems: an Optimal Transport approach,
with Alpar R. Meszaros.
with Olga Turanova, to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire
• Liquid Drops on a Rough surface,
with Will Feldman.
• Congested Aggregation via Newtonian interaction,
with Katy Craig and Yao Yao, Arch. Ration. Mech. Anal. 227 (2018).
with Dohyun Kwon.
• Porous Medium Equation to Hele-Shaw flow with general initial density,
with N. Pozar, Transactions AMS 370 (2018), no.2, 873--909.
• Free boundary problems for Tumor Growth: a Viscosity solutions approach,
with B. Perthame and P. Souganidis, Nonlinear Analysis 138 (2016) (a Special Issue on JL Vazquez's 70th Birthday)
• Continuity and Discontinuity of the boundary layer tail,
with W. Feldman, Ann. Sci. Éc. Norm. Supér. 50 (2017), no. 4, 1017--1064.
• 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.
with S. Choi, Geometric partial differential equations, 105–118, CRM Series, 15, Ed. Norm., Pisa, 2013.
Inwon C. Kim