Weak lower semicontinuity and relaxation for a class of non-local functionals

DOI10.1007/s13163-016-0201-6zbMath1348.49010OpenAlexW2405506590MaRDI QIDQ321237

Pablo Pedregal

Publication date: 13 October 2016

Published in: Revista Matemática Complutense (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13163-016-0201-6

zbMATH Keywords

relaxationvariational problemsseparate convexityweak lower semicontinuitynon-local integral functionals

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Methods involving semicontinuity and convergence; relaxation (49J45)

Related Items (11)

Compactness for a class of integral functionals with interacting local and non-local terms ⋮ Lower semicontinuity and relaxation of nonlocal \(L^\infty\)-functionals ⋮ Γ-limit of the cut functional on dense graph sequences ⋮ A sufficient condition for the lower semicontinuity of nonlocal supremal functionals in the vectorial case ⋮ Extending linear growth functionals to functions of bounded fractional variation ⋮ Lower Semicontinuity and Relaxation Via Young Measures for Nonlocal Variational Problems and Applications to Peridynamics ⋮ Structural changes in nonlocal denoising models arising through bi-level parameter learning ⋮ Loss of Double-Integral Character During Relaxation ⋮ Relaxation of a scalar nonlocal variational problem with a double-well potential ⋮ Quasiconvexity in the fractional calculus of variations: characterization of lower semicontinuity and relaxation ⋮ Cartesian convexity as the key notion in the variational existence theory for nonlocal supremal functionals

Cites Work

• Hyperelasticity as a \(\Gamma\)-limit of peridynamics when the horizon goes to zero
• Characterisation of the weak lower semicontinuity for a type of nonlocal integral functional: the \(n\)-dimensional scalar case
• An introduction to \(\Gamma\)-convergence
• Reformulation of elasticity theory for discontinuities and long-range forces
• Dynamic brittle fracture as a small horizon limit of peridynamics
• Elasticity theory of materials with long range cohesive forces
• Linear theory of nonlocal elasticity and dispersion of plane waves
• Nonlocal Continuum Field Theories
• A necessary and sufficient condition for the weak lower semicontinuity of one-dimensional non-local variational integrals
• On the variational limit of a class of nonlocal functionals related to peridynamics
• Nonlocal variational principles
• Existence for Nonlocal Variational Problems in Peridynamics
• Direct methods in the calculus of variations

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