The limit as \(p\to\infty\) in a two-phase free boundary problem for the \(p\)-Laplacian

DOI10.4171/IFB/359zbMath1344.35060MaRDI QIDQ2630804

Pei-Yong Wang, Julio D. Rossi

Publication date: 22 July 2016

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

zbMATH Keywords

variational principlephase transition\(p\)-Laplacianinfinity Laplaciantwo-phase free boundary problem

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Nonlinear elliptic equations (35J60) Free boundary problems for PDEs (35R35) Variational methods for higher-order elliptic equations (35J35) Quasilinear elliptic equations (35J62) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (6)

A limit case in non-isotropic two-phase minimization problems driven by \(p\)-Laplacians ⋮ The limit as $p\rightarrow \infty $ in free boundary problems with fractional $p$-Laplacians ⋮ An optimization problem with volume constraint with applications to optimal mass transport ⋮ Bernoulli Free Boundary Problem for the Infinity Laplacian ⋮ A limiting free boundary problem with gradient constraint and tug-of-war games ⋮ Regularity properties for p−dead core problems and their asymptotic limit as p→∞

Cites Work

• Unnamed Item
• An optimization problem with free boundary governed by a degenerate quasilinear operator.
• On the Lipschitz regularity of solutions of a minimum problem with free boundary
• A minimum problem with free boundary in Orlicz spaces
• On the uniqueness of a solution of a two-phase free boundary problem
• A free boundary problem for \(\infty\)-Laplace equation
• A minimum problem with free boundary for a degenerate quasilinear operator
• An optimization problem with volume constraint for a degenerate quasilinear operator
• Variational problems with two phases and their free boundaries
• Existence of classical solutions to a free boundary problem for the p-Laplace operator: (II) the interior convex case
• A tour of the theory of absolutely minimizing functions
• Existence of classical solutions to a free boundary problem for the p-Laplace operator: (I) the exterior convex case

This page was built for publication: The limit as \(p\to\infty\) in a two-phase free boundary problem for the \(p\)-Laplacian