The spectral estimates for the Neumann-Laplace operator in space domains

DOI10.1016/j.aim.2017.05.005zbMath1387.35433arXiv1607.00487OpenAlexW2962776705MaRDI QIDQ2362590

Alexander Ukhlov, Vladimir Gol'dshtein

Publication date: 10 July 2017

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.00487

zbMATH Keywords

Sobolev spacesNeumann boundary conditiondiscrete spectrumlinear elliptic equationsgeneralized quasiconformal mappings

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Estimates of eigenvalues in context of PDEs (35P15) Quasiconformal mappings in the complex plane (30C62)

Related Items (12)

Estimates for variation of the first Dirichlet eigenvalue of the Laplace operator ⋮ Space quasiconformal mappings and Neumann eigenvalues in fractal type domains ⋮ Unnamed Item ⋮ Composition operators on Sobolev spaces and \(Q\)-homeomorphisms ⋮ Mappings generating embedding operators in Orlicz-Sobolev spaces ⋮ Sobolev mappings and moduli inequalities on Carnot groups ⋮ On the boundary behavior of weak \((p, q)\)-quasiconformal mappings ⋮ Space quasiconformal composition operators with applications to Neumann eigenvalues ⋮ Composition operators on Hardy-Sobolev spaces and BMO-quasiconformal mappings ⋮ On Lipschitz approximations in second order Sobolev spaces and the change of variables formula ⋮ Composition operators on Sobolev spaces and Neumann eigenvalues ⋮ Space quasiconformal composition operators with applications to Neumann eigenvalues

Cites Work

• Unnamed Item
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• Unnamed Item
• On the first eigenvalues of free vibrating membranes in conformal regular domains
• Spectral estimates of the \(p\)-Laplace Neumann operator in conformal regular domains
• Conformal weights and Sobolev embeddings
• The Beltrami equation. A geometric approach
• An optimal Poincaré inequality for convex domains
• Convexity conditions and existence theorems in nonlinear elasticity
• Extremals for eigenvalues of Laplacians under conformal mapping
• Applications of change of variables operators for exact embedding theorems
• Sharp Poincaré inequalities in a class of non-convex sets
• Homeomorphisms that induce monomorphisms of Sobolev spaces
• On mappings generating the embeddings of Sobolev spaces
• Mappings with bounded \((P,Q)\)-distortion on Carnot groups
• Brennan's conjecture and universal Sobolev inequalities
• On symmetric membranes and conformal radius: Some complements to Polya's and Szegö's inequalities
• A change of variable that preserves the differential properties of functions
• On open and discrete mappings with a modulus condition
• Brennan's conjecture for composition operators on Sobolev spaces
• On some isoperimetric inequalities involving eigenvalues of symmetric free membranes
• Conformal spectral stability estimates for the Dirichlet Laplacian
• Moduli in Modern Mapping Theory
• Weighted Sobolev spaces and embedding theorems
• Sharp Estimates for Eigenfunctions of a Neumann Problem
• ON GEOMETRIC PROPERTIES OF FUNCTIONS WITH GENERALIZED FIRST DERIVATIVES
• Global invertibility of Sobolev functions and the interpenetration of matter
• About homeomorphisms that induce composition operators on Sobolev spaces
• Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems
• Universal Bounds for the Low Eigenvalues of Neumann Laplacians inNDimensions
• NON-LINEAR POTENTIAL THEORY
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
• Superposition operators in Sobolev spaces

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