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 grant DMS-1900804.




    Preprints



 
    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.



 

    Publications 



  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