Estimates for the Sobolev trace constant with critical exponent and applications

DOI10.1007/s10231-007-0062-1zbMath1223.35131arXivmath/0612354OpenAlexW2011589551MaRDI QIDQ931369

Julián Fernández Bonder, Nicolas Saintier

Publication date: 25 June 2008

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612354

zbMATH Keywords

critical exponentsoptimal design problemsSobolev trace embedding

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Variational methods for second-order elliptic equations (35J20) Variational methods for eigenvalues of operators (49Rxx)

Related Items (15)

Some trace Hardy type inequalities and trace Hardy-Sobolev-Maz'ya type inequalities ⋮ Existence of solution to a critical trace equation with variable exponent ⋮ Radiative effects for some bidimensional thermoelectric problems ⋮ Multiplicity of positive solutions for a critical quasilinear Neumann problem ⋮ Optimal boundary holes for the Sobolev trace constant ⋮ Sharp Hardy inequalities in the half space with trace remainder term ⋮ Explicit estimates for solutions of mixed elliptic problems ⋮ Unnamed Item ⋮ Positive and sign-changing solutions for a quasilinear Steklov nonlinear boundary problem with critical growth ⋮ On the Sobolev trace theorem for variable exponent spaces in the critical range ⋮ Estimates of the best Sobolev constant of the embedding of \(\mathrm{BV}(\Omega)\) into \(L^1(\partial \Omega)\) and related shape optimization problems ⋮ The sharp affine \(L^2\) Sobolev trace inequality and variants ⋮ A constrained shape optimization problem in Orlicz-Sobolev spaces ⋮ Asymptotics of best Sobolev constants on thin manifolds ⋮ Explicit estimates for solutions of nonlinear radiation-type problems

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