Research Articles



  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.


    Preprints



   
    with Yuming Zhang, submitted   

  



  Geometry and Stability of normalized mean curvature flow,

         

         with Dohyun Kwon, under revision.


   Publications 




       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