10 citations · 36 across the 15 of their papers we have counts for
17 papers
The sharp interface limit of an Ising game
William M Feldman, Inwon C Kim, Aaron Zeff Palmer
The Ising model of statistical physics has served as a keystone example of phase transitions, thermodynamic limits, scaling laws, and many other phenomena and mathematical methods.…
Quantitative convergence of the "bulk'' free boundary in an oscillatory obstacle problem
Farhan Abedin, William M Feldman
We consider an oscillatory obstacle problem where the coincidence set and free boundary are also highly oscillatory. We establish a rate of convergence for a regularized notion of…
Large scale regularity of almost minimizers of the one-phase problem in periodic media
William M Feldman
We prove that minimizers and almost minimizers of one-phase free boundary energy functionals in periodic media satisfy large scale (1) Lipschitz estimates (2) free boundary flat im…
The occurrence of surface tension gradient discontinuities and zero mobility for Allen-Cahn and curvature flows in periodic media
William M Feldman, Peter S Morfe
We construct several examples related to the scaling limits of energy minimizers and gradient flows of surface energy functionals in heterogeneous media. These include both sharp a…
Recovering coercivity for the G-equation in general random media
William M Feldman
The G-equation is a popular model for premixed turbulent combustion. Mathematically it has attracted a lot of interest in part because it is a simple example of a Hamilton-Jacobi e…
Mean curvature flow with positive random forcing in 2-d
William M Feldman
We consider the forced mean curvature flow in 2-d, finite range of dependence and positive random forcing. We prove flatness and existence of effective speed for initially flat pro…
An example of failure of stochastic homogenization for viscous Hamilton-Jacobi equations without convexity
William M. Feldman, Jean-Baptiste Fermanian, Bruno Ziliotto
We give an example of the failure of homogenization for a viscous Hamilton-Jacobi equation with non-convex Hamiltonian.
Limit shapes of local minimizers for the Alt-Caffarelli energy functional in inhomogeneous media
William M Feldman
This paper considers the Alt-Caffarelli free boundary problem in a periodic medium. This is a convenient model for several interesting phenomena appearing in the study of contact l…
Continuity Properties for Divergence Form Boundary Data Homogenization Problems
William M. Feldman, Yuming Paul Zhang
We study the continuity/discontinuity of the effective boundary condition for periodic homogenization of oscillating Dirichlet data for nonlinear divergence form equations and line…
A free boundary problem with facets
William M Feldman, Charles K Smart
We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamilt…
Stability of Serrin's Problem and Dynamic Stability of a Model for Contact Angle Motion
William M. Feldman
We study the quantitative stability of Serrin's symmetry problem and it's connection with a dynamic model for contact angle motion of quasi-static capillary drops. We prove a new s…
Homogenization and Non-Homogenization of certain Non-Convex Hamilton-Jacobi Equations
William M. Feldman, Panagiotis E. Souganidis
We continue the study of the homogenization of coercive non-convex Hamilton-Jacobi equations in random media identifying two general classes of Hamiltonians with very distinct beha…
Continuity and Discontinuity of the Boundary Layer Tail
William M. Feldman, Inwon C. Kim
We investigate the continuity properties of the homogenized boundary data for oscillating Dirichlet boundary data problems. We show that, for a generic non-rotation-…
Quantitative Homogenization of Elliptic PDE with Random Oscillatory Boundary Data
William M. Feldman, Inwon Kim, Panagiotis E. Souganidis
We study the averaging behavior of nonlinear uniformly elliptic partial differential equations with random Dirichlet or Neumann boundary data oscillating on a small scale. Under co…
An L1 Penalty Method for General Obstacle Problems
Giang Tran, Hayden Schaeffer, William M. Feldman +1
We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like…
Homogenization of the Oscillating Dirichlet Boundary Condition in General Domains
William M. Feldman
We prove the homogenization of the Dirichlet problem for fully nonlinear elliptic operators with periodic oscillation in the operator and of the boundary condition for a general cl…
Dynamic Stability of Equilibrium Capillary Drops
William M. Feldman, Inwon C. Kim
We investigate a model for contact angle motion of quasi-static capillary drops resting on a horizontal plane. We prove global in time existence and long time behavior (convergence…