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 grant DMS-1900804.
• A Hele-Shaw limit without Monotonicity, with Nestor Guillen and Antoine Mellet.
• Well-posedness and Regularity for a Polyconvex Energy, with Wilfrid Gangbo and Matt Jacobs.
• L^1 contraction in Optimal Transport,
with Matt Jacobs and Jiajun Tong, to appear, Ann. Sc. Norm. Super. Pisa Cl. Sci.
• Porous Medium Equation with a Drift: Free boundary regularity,
with Yuming Zhang, to appear, Arch. Ration. Mech. Anal.
• On Volume-preserving Crystaline Mean Curvature Flow,
with Dohyun Kwon and Norbert Pozar, to appear, Mathematische Annalen.
• Darcy’s Law with a Source Term,
with Matt Jacobs and Jiajun Tong, to appear, Arch. Ration. Mech. Anal. 239 no.3 (2021), 1349 - 1393.
• Interface Dynamics in a Two-phase Tumor Growth Model,
with Jiajun Tong. to appear, Interfaces and Free boundaries.
• Weak solutions to the Muskat problem with surface tension via optimal transport,
with Matthew Jacobs and Alpár Mészáros. Arch. Ration. Mech. Anal. 239 no.1 (2021), 389 -430.
• Volume preserving mean curvature flow for star-shaped sets,
with Dohyun Kwon. Cal. Var. and PDE. 59. no.2 (2020),. 1-40.
• Geometry and Stability of normalized mean curvature flow,
with Dohyun Kwon. Comm. PDE. 45, no.5 (2020), 414-455.
• Head and tail speeds of mean curvature flow with forcing,
with Hongwei Gao, Arch. Ration. Mech. Anal. 235, no.1 (2020), 287-354.
• Singular limit of the Porous Medium Equation with a Drift,
with Norbert Pozar and Brent Woodhouse, Advances in Mathematics 349 (2019), 682-732.
with Yuming Zhang, SIAM J. Math. Anal. 50 (2018), no.4, 4371 - 4406.
• On Nonlinear Cross-Diffusion systems: an Optimal Transport approach,
with Alp\’ar R. M\’esz\’aros, Cal. Var. and PDE. 57 (2018), no.3.
with Olga Turanova, Ann. Inst. H. Poincaré Anal. Non Linéaire. 35 (2018), no.5, 1321 - 1354.
• Liquid Drops on a Rough surface,
with Will Feldman, Comm. Pure. Appl. Math. 71 (2018), no.12, 2429 - 2499.
• 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