Spectral estimates of the \(p\)-Laplace Neumann operator in conformal regular domains

DOI10.1016/j.trmi.2016.03.002zbMath1354.35063arXiv1601.01533OpenAlexW2963534174MaRDI QIDQ325145

Alexander Ukhlov, Vladimir Gol'dshtein

Publication date: 17 October 2016

Published in: Transactions of A. Razmadze Mathematical Institute (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.01533

zbMATH Keywords

Sobolev spacesconformal mappingselliptic equations

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Estimates of eigenvalues in context of PDEs (35P15) General theory of conformal mappings (30C35)

Related Items (7)

The spectral estimates for the Neumann-Laplace operator in space domains ⋮ Space quasiconformal mappings and Neumann eigenvalues in fractal type domains ⋮ Composition operators on Sobolev spaces and Neumann eigenvalues ⋮ On variations of the Neumann eigenvalues of \(p\)-Laplacian generated by measure preserving quasiconformal mappings ⋮ Spectral estimates of the \(p\)-Laplace Neumann operator and Brennan's conjecture ⋮ On the first eigenvalue of the degenerate \(p\)-Laplace operator in non-convex domains ⋮ Spectral properties of the Neumann-Laplace operator in quasiconformal regular domains

Cites Work

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• On mappings generating the embeddings of Sobolev spaces
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• Brennan's conjecture and universal Sobolev inequalities
• Brennan's conjecture for composition operators on Sobolev spaces
• Conformal spectral stability estimates for the Dirichlet Laplacian
• Weighted Sobolev spaces and embedding theorems
• The Integrability of the Derivative in Conformal Mapping
• Hölder continuity of conformal maps with quasiconformal extension
• Best constants in Poincar\'e inequalities for convex domains
• Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems
• Superposition operators in Sobolev spaces

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