On the characterization of the compact embedding of Sobolev spaces

DOI10.1007/s00526-011-0441-8zbMath1241.49023arXiv0912.0357OpenAlexW2161329428MaRDI QIDQ425165

Dorin Bucur, Giusseppe Buttazzo

Publication date: 7 June 2012

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0357

zbMATH Keywords

torsional rigiditycompactness of the embeddingspectrum of the Dirichlet Laplacianwell-posedness of a class of geometric inequalities

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Methods involving semicontinuity and convergence; relaxation (49J45) Spectrum, resolvent (47A10) Optimization of shapes other than minimal surfaces (49Q10) Compliance or weight optimization in solid mechanics (74P05)

Related Items (8)

Compact Sobolev embeddings and torsion functions ⋮ Recent Existence Results for Spectral Problems ⋮ Compactness and dichotomy in nonlocal shape optimization ⋮ Schrödinger operators with negative potentials and Lane-Emden densities ⋮ Spectral optimization problems ⋮ Optimal potentials for Schrödinger operators ⋮ Compact embedding results of Sobolev spaces and existence of positive solutions to quasilinear equations ⋮ Compact embedding results of Sobolev spaces and positive solutions to an elliptic equation

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