Preprints

• [arXiv] Minimizing movements solutions for a monotone model of droplet motion
    joint with Carson Collins preprint.


• [arXiv] Regularity theory of a gradient degenerate Neumann problem
    joint with Zhonggan Huang preprint.


• [arXiv] An obstacle approach to rate independent droplet evolution
    joint with Inwon Kim and Norbert Požár preprint.


• [arXiv] On the geometry of rate independent droplet evolution
    joint with Inwon Kim and Norbert Požár preprint.


• [arXiv] Mean curvature flow with positive random forcing in 2-d
    preprint


• [arXiv] Recovering coercivity for the G-equation in general random media
    preprint

Publications

• [arXiv][journal] On convex comparison for exterior Bernoulli problems with discontinuous anisotropy
    joint with Norbert Požár, Interfaces and Free Boundaries (2024).


• [arXiv][journal] The sharp interface limit of an Ising Game
    joint with Inwon Kim and Aaron Zeff Palmer, ESAIM: Control, Optimisation and Calculus of Variations, Volume 30, article 35 (2024).


• [arXiv][journal] Quantitative homogenization of principal Dirichlet eigenvalue shape optimizers
    Communications on Pure and Applied Mathematics.


• [arXiv][journal] Quantitative convergence of the ``bulk'' free boundary in an oscillatory obstacle problem
    joint with Farhan Abedin, Interfaces and Free Boundaries, Vol. 26, No. 1, pp 31-44.


• [arXiv][journal] Large scale regularity of almost minimizers of the one-phase problem in periodic media
    Ars Inveniendi Analytica, Paper No. 2, 41 pp, 2023.


• [arXiv][journal]The occurrence of surface tension gradient discontinuities and zero mobility for Allen-Cahn and curvature flows in periodic media
    joint with Peter Morfe, Interfaces and Free Boundaries, Vol 25, No 4, pp 567-631.


• [arXiv][journal] An example of failure of stochastic homogenization for viscous Hamilton-Jacobi equations without convexity
    joint with J.-B. Fermanian and B. Ziliotto, Journal of Differential Equations, 280: 464-476, 2021.


• [arXiv][journal] Limit shapes of local minimizers for the Alt-Caffarelli functional in inhomogeneous media
    Archive for Rational Mechanics and Analysis, 240: 1255-1322, 2021.


• [arXiv][journal] Continuity properties for divergence form boundary data homogenization problems
    joint with Y. Zhang, Analysis & PDE, 12(8): 1963-2002, 2019.


• [arXiv][journal] A free boundary problem with facets
    joint with C. Smart, Archive for Rational Mechanics and Analysis, 232(1): 389-435, 2019.


• [arXiv][journal] Stability of Serrin's Problem and Dynamic Stability of a Model for Contact Angle Motion
    SIAM Journal on Mathematical Analysis, 50(3): 3303-3326, 2018.


• [arXiv][journal] Liquid Drops on a Rough Surface
    joint with I. Kim, Communications on Pure and Applied Mathematics 71(12): 2429-2499, 2018.


• [arXiv][journal] Homogenization and Non-Homogenization of certain Non-Convex Hamilton-Jacobi Equations
    joint with P. Souganidis, Journal de Mathématiques Pures et Appliquées 108(5): 751-782, 2017 .


• [arXiv][journal] Continuity and Discontinuity of the Boundary Layer Tail
    joint with I. Kim, Annales de l'École Normale Supérieure 50(4): 1017-1064, 2017.


• [arXiv][journal] Quantitative Homogenization of Elliptic PDE with Random Oscillatory Boundary Data
    joint with I. Kim and P. Souganidis, Journal de Mathématiques Pures et Appliquées 103(4): 958-1002, 2015.


• [arXiv][journal] An L1 Penalty Method for General Obstacle Problems
    joint with G. Tran, H. Schaeffer and S. Osher, SIAM J. Appl. Math. 75-4 (2015), pp. 1424-1444.


• [arXiv][journal] Homogenization of the Oscillating Dirichlet Boundary Condition in General Domains
    Journal de Mathématiques Pures et Appliquées, 101(5):599-622, 2014.


• [arXiv][journal] Dynamic Stability of Equilibrium Capillary Drops
    joint with I. Kim, Archive for Rational Mechanics and Analysis, 211(3):819-878, 2014.