On two free boundary problems in potential theory

DOI10.1016/0022-247X(91)90333-UzbMath0760.31003OpenAlexW2043053491MaRDI QIDQ1189674

Lawrence E. Payne, G. A. Philippin

Publication date: 27 September 1992

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(91)90333-u

zbMATH Keywords

solvability theoremsDirichlet and Neumann conditions

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Free boundary problems for PDEs (35R35) Connections of harmonic functions with differential equations in higher dimensions (31B35)

Related Items (16)

Symmetry theorems for some overdetermined boundary value problems on ring domains ⋮ On some second order and fourth order elliptic overdetermined problems ⋮ A duality theorem for an overdetermined eigenvalue problem ⋮ Constrained radial symmetry for the infinity-Laplacian ⋮ On a free boundary problem for the \(p\)-Laplacian ⋮ The isoperimetric inequality via approximation theory and free boundary problems ⋮ On gradient maximum principles for quasilinear elliptic equations ⋮ Overdetermined problems in annular domains with a spherical-boundary component in space forms ⋮ Symmetry results for Serrin-type problems in doubly connected domains ⋮ Overdetermined Neumann boundary value problem in unbounded domains ⋮ A local symmetry result for linear elliptic problems with solutions changing sign ⋮ On the radial symmetry property for harmonic functions ⋮ A free boundary problem with multiple boundaries for a general class of anisotropic equations ⋮ Symmetry for an overdetermined boundary problem in a punctured domain ⋮ Some fully nonlinear elliptic boundary value problems with ellipsoidal free boundaries ⋮ Boundary point lemmas and overdetermined problems.

Cites Work

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• Some remarks on overdetermined systems in linear elasticity
• A symmetry problem in potential theory
• Remark on the preceding paper of Serrin
• On the torsional rigidity of multiply connected cross-sections
• Duality theorems in some overdetermined boundary value problems
• On a free boundary problem in electrostatics
• Symmetry in an Overdetermined Fourth Order Elliptic Boundary Value Problem
• Convexity properties for solutions of some second order elliptic semilinear equations
• Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature
• A Symmetry Result Related to Some Overdetermined Boundary Value Problems
• Isoperimetric Inequalities and Their Applications
• A Remark on Linear Elliptic Differential Equations of Second Order

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