The Saint-Venant inequality for the Laplace operator with Robin boundary conditions

DOI10.1007/s00032-015-0243-0zbMath1334.35183OpenAlexW2183710234MaRDI QIDQ901836

Alessandro Giacomini, Dorin Bucur

Publication date: 6 January 2016

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-015-0243-0

zbMATH Keywords

shape optimizationFaber-Krahn inequalityRobin-LaplacianSaint-Venant inequality

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Estimates of eigenvalues in context of PDEs (35P15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (9)

Inequalities for the fundamental Robin eigenvalue for the Laplacian on N-dimensional rectangular parallelepipeds ⋮ Compactness of \(M\)-uniform domains and optimal thermal insulation problems ⋮ Sharp estimates for the Gaussian torsional rigidity with Robin boundary conditions ⋮ Comparison results for solutions of Poisson equations with Robin boundary on complete Riemannian manifolds ⋮ A rigidity result for the Robin torsion problem ⋮ A free boundary approach to the Faber-Krahn inequality ⋮ An optimal bound for nonlinear eigenvalues and torsional rigidity on domains with holes ⋮ Sharp estimates for the first p-Laplacian eigenvalue and for the p-torsional rigidity on convex sets with holes ⋮ Stability analysis on two thermal insulation problems

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