The best Sobolev trace constant in domains with holes for critical or subcritical exponents

DOI10.1017/S1446181100012797zbMath1144.35338MaRDI QIDQ3505057

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Publication date: 18 June 2008

Published in: The ANZIAM Journal (Search for Journal in Brave)

zbMATH Keywords

nonlinear boundary conditionsperiodically distributed holes

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Critical exponents in context of PDEs (35B33) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (3)

The best Sobolev trace constant in a domain with oscillating boundary ⋮ A constrained shape optimization problem in Orlicz-Sobolev spaces ⋮ Where to place a spherical obstacle so as to maximize the first nonzero Steklov eigenvalue

Cites Work

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• Problèmes de Neumann non linéaires sur les variétés riemanniennes
• On the best Sobolev trace constant and extremals in domains with holes
• Homogenization in open sets with holes
• Potential and scattering theory on wildly perturbed domains
• Best constants in Sobolev trace inequalities
• A convex-concave problem with a nonlinear boundary condition.
• Symmetry properties for the extremals of the Sobolev trace embedding
• Regularity of the Free Boundary in an Optimization Problem Related to the Best Sobolev Trace Constant
• Positive solution for neumann problem with critical non linearity on boundary
• ON VIBRATIONS OF A BODY WITH MANY CONCENTRATED MASSES NEAR THE BOUNDARY
• ON THE EXISTENCE OF EXTREMALS FOR THE SOBOLEV TRACE EMBEDDING THEOREM WITH CRITICAL EXPONENT
• VIBRATIONS OF A MEMBRANE WITH MANY CONCENTRATED MASSES NEAR THE BOUNDARY

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