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-2153254.




    Preprints


     The sharp interface limit of an Ising game


    with Will Feldman and Aaron Palmer.



  
  Tumor growth with nutrients: stability of the tumor patches


     with Jona Lelmi.


     Regularity of Hele-Shaw Flow with source and drift

     with Yuming Zhang.


  

       Incompressible limit of PME with bistable and monostable reaction terms


     with Antoine Mellet.



       The Stefan problem and Free Targets of Optimal brownian martingale Transport, 


   with Young-Heon Kim.



 
    Well-posedness and Regularity for a Polyconvex Energy,  


   with Wilfrid Gangbo and Matt Jacobs.



 

    Publications 




     
with Matt Jacobs and Jiajun Tong,   Comm. AMS.



    Density constrained Chemotaxis and Hele-Shaw flow


       with Antoine Mellet and Yijing Wu,   Transactions AMS.


  A density-constrained model for Chemotaxis


       with Antoine Mellet and Yijing Wu, to appear, Nonlinearity.

  


     A Hele-Shaw limit without Monotonicity,  


    with Nestor Guillen and Antoine Mellet,  Arch. Ration. Mech. Anal. 243, no.2 (2022), 829-868.



  L^1 contraction in Optimal Transport,   


    with Matt Jacobs and Jiajun Tong,   Ann. Sc. Norm. Super. Pisa Cl. Sci. (2022), p. 1817-1919.



      Porous Medium Equation with a Drift: Free boundary regularity,  


    with Yuming Zhang,  Arch. Ration. Mech. Anal. (2021), p 1-52.




    On Volume-preserving Crystaline Mean Curvature Flow, 


   with Dohyun Kwon and Norbert Pozar,  Mathematische Annalen.  384 no.1 (2022), 1-42.



   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.  Interfaces and Free boundaries. vol. 23, no. 2 (2021), 191-304.



     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.


    Homogenization of oblique boundary value problems,  

        

         with Sunhi Choi, to appear in Adv. Nonlinear studies, for David Jerison’s  70th Birthday.



       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