Quasiconvexity in the fractional calculus of variations: characterization of lower semicontinuity and relaxation

DOI10.1016/j.na.2021.112625zbMath1478.49011arXiv2104.04833OpenAlexW3209960766WikidataQ114013626 ScholiaQ114013626MaRDI QIDQ2057919

Carolin Kreisbeck, Hidde Schönberger

Publication date: 7 December 2021

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.04833

zbMATH Keywords

quasiconvexityrelaxationfractional Sobolev spacesweak lower semicontinuitynonlocal variational problemsRiesz fractional gradient

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Fractional partial differential equations (35R11)

Related Items (8)

Leibniz rules and Gauss-Green formulas in distributional fractional spaces ⋮ Failure of the local chain rule for the fractional variation ⋮ Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups ⋮ Non-local gradients in bounded domains motivated by continuum mechanics: fundamental theorem of calculus and embeddings ⋮ Extending linear growth functionals to functions of bounded fractional variation ⋮ On a special class of non-local variational problems ⋮ Cartesian convexity as the key notion in the variational existence theory for nonlocal supremal functionals ⋮ The fractional variation and the precise representative of \(BV^{\alpha,p}\) functions

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