127 citations · 200 across the 14 of their papers we have counts for
22 papers
The homogeneous and inhomogeneous Dirichlet problem
David S. Jerison, Carlos E. Kenig
We revisit the homogeneous and inhomogeneous Dirichlet problem for the Laplacian on Lipschitz domains. This is motivated by the recent postings by Amrouche and Moussaoui which purp…
Inhomogeneous global minimizers to the one-phase free boundary problem
Daniela De Silva, David Jerison, Henrik Shahgholian
Given a global 1-homogeneous minimizer to the Alt-Caffarelli energy functional, with , we provide a foliation of the half-space $\R^{n} \times [0,+\inft…
The Friedland-Hayman inequality and Caffarelli's contraction theorem
Thomas Beck, David Jerison
The Friedland-Hayman inequality is a sharp inequality concerning the growth rates of homogeneous, harmonic functions with Dirichlet boundary conditions on complementary cones divid…
Two-phase free boundary problems in convex domains
Thomas Beck, David Jerison, Sarah Raynor
We study the regularity of minimizers of a two-phase free boundary problem. For a class of n-dimensional convex domains, we establish the Lipschitz continuity of the minimizer up t…
Free boundaries subject to topological constraints
David S. Jerison, Nikola Kamburov
We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamen…
The Two Hyperplane Conjecture
David Jerison
We introduce a conjecture that we call the {\it Two Hyperplane Conjecture}, saying that an isoperimetric surface that divides a convex body in half by volume is trapped between par…