Relaxation and optimal finiteness domain for degenerate quadratic functionals. One-dimensional case

DOI10.1051/COCV/2024022MaRDI QIDQ6491782

Virginia De Cicco, Francesco Serra Cassano

Publication date: 24 April 2024

Published in: European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations (Search for Journal in Brave)

zbMATH Keywords

relaxationlower semicontinuityPoincaré inequalityweightdegenerate variational integrals

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Methods involving semicontinuity and convergence; relaxation (49J45)

Cites Work

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• Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
• Density of smooth functions in weighted Sobolev spaces
• Closure of the set of diffusion functionals -- the one-dimensional case
• \(L^ 2-\)lower semicontinuity of functionals of quadratic type
• An approach to the asymptotic behaviour of elliptic-parabolic operators
• Relaxation of a quadratic functional defined by a nonnegative unbounded matrix
• Differentiability of Lipschitz functions on metric measure spaces
• Composite media and asymptotic Dirichlet forms
• On the variational convergence of non-coercive quadratic integral functionals and semicontinuity problems
• Weighted Sobolev spaces on metric measure spaces
• A Saint-Venant type principle for Dirichlet forms on discontinuous media
• Tensorization of Cheeger energies, the space \(H^{1, 1}\) and the area formula for graphs
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Nonlocal effects in two-dimensional conductivity
• Heat Flow and Calculus on Metric Measure Spaces with Ricci Curvature Bounded Below—The Compact Case
• The local regularity of solutions of degenerate elliptic equations
• CLOSURE OF THE SET OF DIFFUSION FUNCTIONALS WITH RESPECT TO THE MOSCO-CONVERGENCE
• Sobolev Spaces on Metric Measure Spaces
• Admissible measures in one dimension

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