Uniform concentration-compactness for Sobolev spaces on variable domains

DOI10.1006/jdeq.1999.3726zbMath0957.49027OpenAlexW2087025557MaRDI QIDQ1566847

Dorin Bucur

Publication date: 11 March 2001

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3726

zbMATH Keywords

shape optimizationconcentration-compactness principlegamma convergenceresolvent operators

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Methods involving semicontinuity and convergence; relaxation (49J45) Optimization of shapes other than minimal surfaces (49Q10) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (11)

Local and global uniform convergence for elliptic problems on varying domains ⋮ A variational study of some hadron bag models ⋮ Existence of nonradial domains for overdetermined and isoperimetric problems in nonconvex cones ⋮ Recent Existence Results for Spectral Problems ⋮ Regularity of minimizers of shape optimization problems involving perimeter ⋮ Compactness and dichotomy in nonlocal shape optimization ⋮ Spectral optimization problems with internal constraint ⋮ Minimization of the \(k\)-th eigenvalue of the Dirichlet Laplacian ⋮ Optimization results for the higher eigenvalues of the p‐Laplacian associated with sign‐changing capacitary measures ⋮ Existence and regularity of minimizers for some spectral functionals with perimeter constraint ⋮ Dirichlet problems on varying domains.

Cites Work

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