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 currently supported by NSF analysis program DMS-1566578.
with Norbert Pozar and Brent Woodhouse.
• On Nonlinear Cross-Diffusion systems: an Optimal Transport approach,
with A. R. Meszaros.
with O. Turanova.
• Liquid Drops on a Rough surface,
with W. Feldman.
• Congested Aggregation via Newtonian interaction,
with K. Craig and Y. Yao, to appear in Arch. Ration. Mech. Anal.
with D. Kwon.
• Porous Medium Equation to Hele-Shaw flow with general initial density,
with N. Pozar, to appear in Transactions AMS.
• Free boundary problems for Tumor Growth: a Viscosity solutions approach,
with B. Perthame and P. Souganidis, Nonlinear Analysis (2016), a Special Issue on the occasion of JL Vazquez's 70th Birthday.
• Continuity and Discontinuity of the boundary layer tail,
with W. Feldman, to appear Ann. Sci. Éc. Norm. Supér.
• 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