Some properties of functionals on level sets

DOI10.13108/2019-11-2-114zbMath1463.28006OpenAlexW2963503633MaRDI QIDQ5137835

R. G. Salakhudinov

Publication date: 2 December 2020

Published in: Ufimskii Matematicheskii Zhurnal (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/ufa475

zbMATH Keywords

isoperimetric inequalitywarping functiondistance to boundaryisoperimetric monotonicityPayne-type inequality

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Length, area, volume, other geometric measure theory (28A75) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Cites Work

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• Hardy type inequalities in higher dimensions with explicit estimate of constants
• Two-sided estimates of \(L^p\)-norms of the stress function for convex domains in \(\mathbb R^n\)
• Integral properties of the classical warping function of a simply connected domain
• Payne type inequalities for \(L^p\)-norms of the warping functions
• Isoperimetric inequalities for \(L^p\)-norms of the stress function of a multiply connected plane domain
• Isoperimetric properties of Euclidean boundary moments of a simply connected domain
• Torsional Rigidity and Expected Lifetime of Brownian Motion
• Refined Inequalities for Euclidean Moments of a Domain with Respect to Its Boundary
• Solution of the generalized Saint Venant problem
• The co-area formula for Sobolev mappings
• Isoperimetric Inequalities in Mathematical Physics. (AM-27)

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