The best constant and extremals of the Sobolev embeddings in domains with holes: the \(L^{\infty }\) case

zbMath1181.49006MaRDI QIDQ2654668

Julio D. Rossi, Julián Fernández Bonder, Carola-Bibiane Schönlieb

Publication date: 20 January 2010

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

Full work available at URL: https://projecteuclid.org/euclid.ijm/1258554352

zbMATH Keywords

Sobolev trace embeddinggeometrical characterization of this optimal hole

Mathematics Subject Classification ID

Variational inequalities (49J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational problems in a geometric measure-theoretic setting (49Q20) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

Related Items (2)

Monotonicity of the principal eigenvalue related to a non-isotropic vibrating string ⋮ A constrained shape optimization problem in Orlicz-Sobolev spaces

Cites Work

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• ASYMPTOTIC BEHAVIOR OF BEST CONSTANTS AND EXTREMALS FOR TRACE EMBEDDINGS IN EXPANDING DOMAINS1*
• SYMMETRY AND SYMMETRY BREAKING FOR MINIMIZERS IN THE TRACE INEQUALITY
• Regularity of the Free Boundary in an Optimization Problem Related to the Best Sobolev Trace Constant
• The 𝐴𝐵 program in geometric analysis: sharp Sobolev inequalities and related problems
• A tour of the theory of absolutely minimizing functions
• Minimizing theL^∞Norm of the Gradient with an Energy Constraint

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