Regularity of a free boundary with application to the Pompeiu problem
From MaRDI portal
Publication:1972074
DOI10.2307/121117zbMath0960.35112arXivmath/0010016OpenAlexW2006686176MaRDI QIDQ1972074
Lavi Karp, Henrik Shahgholian, Luis A. Caffarelli
Publication date: 10 May 2001
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0010016
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Free boundary problems for PDEs (35R35) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)
Related Items
Regularity properties of a free boundary near contact points with the fixed boundary., Regularity of a free boundary at the infinity point, Boundary behaviour for a singular perturbation problem, Eliminating Mixed Asymptotics in Obstacle Type Free Boundary Problems, Generic regularity of free boundaries for the obstacle problem, Solutions of fully nonlinear elliptic equations with patches of zero gradient: Existence, regularity and convexity of level curves, Analysis of the free boundary for the \(p\)-parabolic variational problem \((p\geq 2)\), Infinity Laplacian equations with singular absorptions, Properties of the free boundary near the fixed boundary of the double obstacle problems, Spherical spectral synthesis and two-radius theorems on Damek-Ricci spaces, On the singular set of the parabolic obstacle problem, On the regularity of a free boundary near contact points with a fixed boundary, The behavior of the free boundary near the fixed boundary for a minimization problem, Regularity of a free boundary in parabolic potential theory, Symmetry theorems for the overdetermined eigenvalue problems, Unnamed Item, Regularity of a free boundary for viscosity solutions of nonlinear elliptic equations, Rellich type identities for eigenvalue problems and application to the Pompeiu problem, Boundary regularity for a parabolic obstacle type problem, New monotonicity formulae for semi-linear elliptic and parabolic systems, Geometric approach to nonvariational singular elliptic equations, The regularity theory for the double obstacle problem, Fully nonlinear free transmission problems, The structure of the regular part of the free boundary close to singularities in the obstacle problem, An overview of unconstrained free boundary problems, Quadrature for quadrics, Scaling limits for internal aggregation models with multiple sources, The regularity theory for the double obstacle problem for fully nonlinear operator, On global solutions of the obstacle problem, Properties of the free boundaries for the obstacle problem of the porous medium equations, Hausdorff measure and stability for the \(p\)-obstacle problem \((2<p<\infty)\)., A new discrete monotonicity formula with application to a two-phase free boundary problem in dimension two, Overdetermined Neumann boundary value problem in unbounded domains, On the Lipschitz regularity of solutions of a minimum problem with free boundary, On null quadrature domains, On the non-tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem, Optimal regularity for phase transition problems with convection, The regularity theory for the parabolic double obstacle problem, Tangential Touch Between Free and Fixed Boundaries in a Problem from Superconductivity, Optimal Regularity for the No‐Sign Obstacle Problem, Radial symmetry for an elliptic PDE with a free boundary, On the Lipschitz regularity and asymptotic behaviour of the free boundary for classes of minima of inhomogeneous two-phase alt-caffarelli functionals in Orlicz spaces, Tangential touch between the free and the fixed boundary in a semilinear free boundary problem in two dimensions, A parabolic almost monotonicity formula, Asymptotic estimates for the spatial segregation of competitive systems, On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae, Regularity estimates for fully non linear elliptic equations which are asymptotically convex, Optimal regularity in the obstacle problem for Kolmogorov operators related to American Asian options, Regularity near the initial state in the obstacle problem for a class of hypoelliptic ultraparabolic operators, Erratum to ``On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients, Uniform regularity close to cross singularities in an unstable free boundary problem, The two-phase membrane problem--an intersection-comparison approach to the regularity at branch points, Obstacle problem for a non-convex fully nonlinear operator, Topology of quadrature domains, Regularity of a Parabolic Free Boundary Problem with Hölder Continuous Coefficients, Pointwise estimates for Laplace equation. Applications to the free boundary of the obstacle problem with Dini coefficients, On the tangential touch between the free and the fixed boundaries for the two-phase obstacle-like problem, Capillary surfaces arising in singular perturbation problems, A free boundary problem associated with the isoperimetric inequality, Monotonicity formulas for obstacle problems with Lipschitz coefficients, Potential theory and approximation: highlights from the scientific work of Stephen Gardiner, The zero level set for a certain weak solution, with applications to the Bellman equations, Non-transversal intersection of the free and fixed boundary in the mean-field theory of superconductivity, Analysis of a free boundary at contact points with Lipschitz data, Characterizing compact coincidence sets in the obstacle problem—a short proof, Optimal regularity of solutions to no-sign obstacle-type problems for the sub-Laplacian, Global solutions of the obstacle problem in half-spaces, and their impact on local stability, Quadrature Domains and Their Two-Phase Counterparts, Equilibrium points of a singular cooperative system with free boundary, A general class of free boundary problems for fully nonlinear parabolic equations, An optimal partition problem related to nonlinear eigenvalues.
