On a Class of Overdetermined Eigenvalue Problems

DOI<905::AID-MMA890>3.0.CO;2-8 10.1002/(SICI)1099-1476(19970725)20:11<905::AID-MMA890>3.0.CO;2-8zbMath0881.35082OpenAlexW2066763160MaRDI QIDQ4347610

G. A. Philippin, Antoine Henrot

Publication date: 7 August 1997

Full work available at URL: https://doi.org/10.1002/(sici)1099-1476(19970725)20:11<905::aid-mma890>3.0.co;2-8

zbMATH Keywords

Steiner symmetrizationsymmetry for inhomogeneous Dirichlet eigenvalue problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Invariance and symmetry properties for PDEs on manifolds (58J70) Free boundary problems for PDEs (35R35) Overdetermined systems of PDEs with variable coefficients (35N10) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items (7)

Unnamed Item ⋮ A sharp upper bound for the first Dirichlet eigenvalue of a class of wedge-like domains ⋮ Pointwise and \(L_{2}\) bounds in some nonstandard problems for the heat equation ⋮ Isoperimetric inequalities for a wedge-like membrane ⋮ Symmetry for a general class of overdetermined elliptic problems ⋮ Weinstein's Technique for a Class of Parabolic Problems ⋮ A symmetry result for an overdetermined elliptic problem using continuous rearrangement and domain derivative

Cites Work

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• Some remarks on overdetermined systems in linear elasticity
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• On the convexity of level lines of the fundamental mode in the clamped membrane problem, and the existence of convex solutions in a related free boundary problem
• A general rearrangement inequality for multiple integrals
• A symmetry problem in potential theory
• Symmetry Theorems Related to Pompeiu's Problem
• Differentiation with Respect to the Domain in Boundary Value Problems
• Convexity properties of solutions to some classical variational problems
• Continuous Steiner‐Symmetrization
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)

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