Weighted isoperimetric inequalities in cones and applications

DOI10.1016/j.na.2012.05.011zbMath1253.26049arXiv1107.5406OpenAlexW2039146889MaRDI QIDQ441166

Anna Mercaldo, Francesco Chiacchio, Friedemann Brock

Publication date: 20 August 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.5406

zbMATH Keywords

degenerate elliptic equationsHardy inequalitiesrelative isoperimetric inequalitiesNeumann eigenvaluesBeltrami operatorweighted Laplace

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Degenerate elliptic equations (35J70) Other analytical inequalities (26D20)

Related Items (18)

An isoperimetric inequality for Gauss-like product measures ⋮ A remark on optimal weighted Poincaré inequalities for convex domains ⋮ Isoperimetric sets for weighted twisted eigenvalues ⋮ A sharp upper bound for the first Dirichlet eigenvalue of a class of wedge-like domains ⋮ An overview on extremals and critical points of the Sobolev inequality in convex cones ⋮ Volume growth and on-diagonal heat kernel bounds on Riemannian manifolds with an end ⋮ Neumann comparison theorems in elliptic PDEs ⋮ Optimal Szegő-Weinberger type inequalities ⋮ Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities ⋮ Isoperimetric inequalities for a wedge-like membrane ⋮ Sharp isoperimetric inequalities via the ABP method ⋮ Euclidean balls solve some isoperimetric problems with nonradial weights ⋮ The isoperimetric problem for a class of non-radial weights and applications ⋮ A weighted isoperimetric inequality in an orthant ⋮ Some weighted isoperimetric problems on \({\mathbb{R}}^N_+\) with stable half balls have no solutions ⋮ On weighted isoperimetric inequalities with non-radial densities ⋮ Symmetry breaking in a constrained Cheeger type isoperimetric inequality ⋮ Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift

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