On the torsion function with mixed boundary conditions

DOI10.1007/s11118-020-09857-1zbMath1479.35311arXiv1911.02336OpenAlexW3010041045MaRDI QIDQ2048846

Tom Carroll, Michiel van den Berg

Publication date: 24 August 2021

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.02336

zbMATH Keywords

Dirichlet boundary conditionNeumann boundary conditiontorsion function

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Cites Work

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• Estimate on the fundamental frequency of a drum
• The first eigenvalue of the Laplacian on two dimensional Riemannian manifolds
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• \(L_\infty\)-estimates for the torsion function and \(L_{\infty}\)-growth of semigroups satisfying Gaussian bounds
• Traps for reflected Brownian motion
• Principal eigenvalue estimates via the supremum of torsion
• Hardy inequality and L ^p estimates for the torsion function