David Jerison
YOU?
Author Swipe
View article: Inhomogeneous global minimizers to the one-phase free boundary problem
Inhomogeneous global minimizers to the one-phase free boundary problem Open
Given a global 1-homogeneous minimizer U0 to the Alt-Caffarelli energy functional, with sing(F(U0))={0}, we provide a foliation of the half-space Rn×[0,+∞) with dilations of graphs of global minimizers U¯≤U0≤U¯ with analytic free boundarie…
View article: The Friedland–Hayman inequality and Caffarelli’s contraction theorem
The Friedland–Hayman inequality and Caffarelli’s contraction theorem Open
The Friedland–Hayman inequality is a sharp inequality concerning the growth rates of homogeneous, harmonic functions with Dirichlet boundary conditions on complementary cones dividing Euclidean space into two parts. In this paper, we prove…
View article: Inhomogeneous global minimizers to the one-phase free boundary problem
Inhomogeneous global minimizers to the one-phase free boundary problem Open
Given a global 1-homogeneous minimizer $U_0$ to the Alt-Caffarelli energy functional, with $sing(F(U_0)) = \{0\}$, we provide a foliation of the half-space $\R^{n} \times [0,+\infty)$ with dilations of graphs of global minimizers $\underli…
View article: On nonminimizing solutions of elliptic free boundary problems
On nonminimizing solutions of elliptic free boundary problems Open
We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and subcri…
View article: Computing Spectra without Solving Eigenvalue Problems
Computing Spectra without Solving Eigenvalue Problems Open
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computatio…
View article: Free boundaries subject to topological constraints
Free boundaries subject to topological constraints Open
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 fundamental work of Luis Caffarelli on free boundaries and by strik…
View article: Higher critical points in a free boundary problem
Higher critical points in a free boundary problem Open
We study higher critical points of the variational functional associated with a free boundary problem related to plasma confinement. Existence and regularity of minimizers in elliptic free boundary problems have already been studied extens…
View article: Effective Confining Potential of Quantum States in Disordered Media
Effective Confining Potential of Quantum States in Disordered Media Open
The amplitude of localized quantum states in random or disordered media may exhibit long-range exponential decay. We present here a theory that unveils the existence of an effective potential which finely governs the confinement of these s…
View article: Structure of One-Phase Free Boundaries in the Plane
Structure of One-Phase Free Boundaries in the Plane Open
We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply-connected. We show that if two components of the free boundary are…
View article: Effective confining potential of quantum states in disordered media
Effective confining potential of quantum states in disordered media Open
The amplitude of localized quantum states in random or disordered media may exhibit long range exponential decay. We present here a theory that unveils the existence of an effective potential which finely governs the confinement of these s…
View article: Quantitative stability for sumsets in $\mathbb R^n$
Quantitative stability for sumsets in $\mathbb R^n$ Open
Given a measurable set A\subset \mathbb R^n of positive measure, it is not difficult to show that |A+A|=|2A| if and only if A is equal to its convex hull minus a set of measure zero. We investigate the stability of this statement: If (|A+A…
View article: Quantitative stability for sumsets in R[superscript n]
Quantitative stability for sumsets in R[superscript n] Open
Given a measurable set A ⊂ ℝ[superscript n] of positive measure, it is not difficult to show that |A + A| = |2A| if and only if A is equal to its convex hull minus a set of measure zero. We investigate the stability of this statement: If (…