On a Poincaré type formula for solutions of singular and degenerate elliptic equations

DOI10.1007/s00229-010-0349-1zbMath1195.35155OpenAlexW2018189512MaRDI QIDQ981653

Alberto Farina, Berardino Sciunzi, Enrico Valdinoci

Publication date: 2 July 2010

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-010-0349-1

zbMATH Keywords

degenerate elliptic equationsstable solutionsPoincaré type formula

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Stability in context of PDEs (35B35) Degenerate elliptic equations (35J70) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Singular elliptic equations (35J75) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (12)

Stable solutions of elliptic equations on Riemannian manifolds ⋮ Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces ⋮ Classification of stable solutions for boundary value problems with nonlinear boundary conditions on Riemannian manifolds with nonnegative Ricci curvature ⋮ Boundedness of stable solutions to nonlinear equations involving the \(p\)-Laplacian ⋮ Stable solutions of symmetric systems on Riemannian manifolds ⋮ Symmetry properties for solutions of nonlocal equations involving nonlinear operators ⋮ Monotonicity and one-dimensional symmetry for solutions of \(-\Delta_{p}u = f(u)\) in half-spaces ⋮ Symmetry results for nonlinear elliptic operators with unbounded drift ⋮ Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces ⋮ Regularity of the extremal solution for singular \(p\)-Laplace equations ⋮ Monotonicity results in half-spaces for thep-Laplacian ⋮ Optimal regularity of stable solutions to nonlinear equations involving the \(p\)-Laplacian

Cites Work

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• On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property

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