The one phase free boundary problem for the $p$-Laplacian with non-constant Bernoulli boundary condition

DOI10.1090/S0002-9947-02-02892-1zbMath0988.35174OpenAlexW1709282685MaRDI QIDQ2781412

Henrik Shahgholian, Antoine Henrot

Publication date: 19 March 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-02-02892-1

zbMATH Keywords

\(p\)-Laplacianconvex solutionsboundary gradient conditionexterior and interior free boundary problemnonlinear joining conditions

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Degenerate elliptic equations (35J70) Free boundary problems for PDEs (35R35)

Related Items (10)

A Bernoulli problem with non-constant gradient boundary constraint ⋮ A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition ⋮ Concavity properties for elliptic free boundary problems ⋮ Linear stability analysis of overdetermined problems with non-constant data ⋮ On a two-phase Serrin-type problem and its numerical computation ⋮ Symmetry theorems and uniform rectifiability ⋮ A free boundary problem for \(p\)-Laplacian in the plane ⋮ On a Bernoulli problem with geometric constraints ⋮ Uniqueness in a Free Boundary Problem ⋮ Bernoulli's problem for the infinity-Laplacian near a set with positive reach

Cites Work

• Degenerate parabolic equations
• A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\)
• Capacitary functions in convex rings
• A free boundary problem for \(\infty\)-Laplace equation
• A symmetry problem in potential theory
• On The Dirichletproblem for Quasilinear Equations
• On quasilinear elliptic equations in domains with conical boundary points.
• A Harnack inequality approach to the regularity of free boundaries part II: Flat free boundaries are Lipschitz
• Uniform estimates and limits for a two phase parabolic singular perturbation problem
• The inverse function theorem of Nash and Moser
• Regularity of the free boundary for the porous medium equation
• On the existence of convex classical solutions for multilayer free boundary problems with general nonlinear joining conditions
• On gradient maximum principles for quasilinear elliptic equations
• Existence of classical solutions to a free boundary problem for the p-Laplace operator: (II) the interior convex case
• Convexity properties of solutions to some classical variational problems
• Existence of classical solutions to a free boundary problem for the p-Laplace operator: (I) the exterior convex case
• Convexity of free boundaries with bernoulli type boundary condition
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The one phase free boundary problem for the $p$-Laplacian with non-constant Bernoulli boundary condition