On the relaxation in \(BV(\Omega ;\mathbb{R}^ m)\) of quasi-convex integrals

From MaRDI portal
Publication:1207127

DOI10.1016/0022-1236(92)90012-8zbMath0769.49009OpenAlexW2065343760MaRDI QIDQ1207127

Gianni Dal Maso, Luigi Ambrosio

Publication date: 2 May 1993

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(92)90012-8




Related Items (74)

Lower semicontinuity and Young measures in BV without Alberti's Rank-One TheoremOn the singular part of measures constrained by linear PDEs and applicationsFine properties of functions of bounded deformation -- an approach via linear PDEsLoss of polyconvexity by homogenizationHomogenization of variational problems in manifold valued \(BV\)-spacesRelaxation of functionals in the space of vector-valued functions of bounded HessianA BV functional and its relaxation for joint motion estimation and image sequence recoveryA note on Meyers’ Theorem in $W^{k,1}$\(\mathcal A\)-quasiconvexity: weak-star convergence and the gapLower semicontinuity for an integral functional in BVA relaxation result for micromagnetics in SBVStability and experimental comparison of prototypical iterative schemes for total variation regularized problemsA global method for deterministic and stochastic homogenisation in \textit{BV}Relaxation of variational problems under trace constraintsHomogenization of integral functionals with linear growth defined on vector-valued functionsRelaxation of signed integral functionals in BVReal-Time Adaptive Video CompressionRelaxation in \(BV\) versus quasiconvexification in \(W^{1,p}\); a model for the interaction between fracture and damagePartial regularity for \(\omega\)-minimizers of quasiconvex functionalsAn Image Registration Model in Electron Backscatter DiffractionOn the structure of \({\mathcal A}\)-free measures and applicationsLower semicontinuity and relaxation of signed functionals with linear growth in the context of \(\mathcal A\)-quasiconvexityHomogenization of vector-valued partition problems and dislocation cell structures in the planeHomogenization problems in the calculus of variations: an overviewMinimization to the Zhang's energy on \(BV (\Omega)\) and sharp affine Poincaré-Sobolev inequalitiesA chromaticity-brightness model for color images denoising in a Meyer's ``\(u + v\) frameworkFunctions of bounded variation on ``good metric spacesAnisotropic singular perturbations—the vectorial caseRelaxation of certain integral functionals depending on strain and chemical compositionA two-gradient approach for phase transitions in thin filmsThe interaction between bulk energy and surface energy in multiple integralsOn the lower semicontinuity of quasiconvex integrals in SBV(Ω, Rk)Stochastic homogenization of degenerate integral functionals with linear growthOn the relaxation of functionals with contact terms on non-smooth domainsA relaxation result in B V × L p for integral functionals depending on chemical composition and elastic strainMichell trusses in two dimensions as a \(\Gamma \)-limit of optimal design problems in linear elasticityRelaxation of functionals with linear growth: interactions of emerging measures and free discontinuitiesClosure result for \(\Gamma\)-limits of functionals with linear growthHomogenization of functionals with linear growth in the context of \(\mathcal A\)-quasiconvexityExtending linear growth functionals to functions of bounded fractional variationPhase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energyRelaxation in SBV\(_{p } (\varOmega ; S ^{d-1})\)On the Integral Representation of Variational Functionals on $BD$Unnamed ItemRelaxation for Partially Coercive Integral Functionals with Linear GrowthLower semicontinuity in Sobolev spaces below the growth exponent of the integrandPartial regularity for symmetric quasiconvex functionals on BDA geometric maximum principle for variational problems in spaces of vector-valued functions of bounded variationObstacle Problems with Linear Growth: Hölder Regularity for the Dual SolutionExistence for evolutionary problems with linear growth by stability methodsSimple proofs of some results of ReshetnyakLiftings, Young measures, and lower semicontinuityPartial regularity for BV minimizersExistence theorems for discontinuous solutions in optimization problemsA note about weak \(\ast\) lower semicontinuity for functionals with linear growth in \(W^{1,1} \times L^1\)Relaxation of quasiconvex functionals in \(BV(\Omega, \mathbb{R}^ N)\) for integrands \(f(x, u, \bigtriangledown u)\)Relaxation of multidimensional variational problems with constraints of general formLower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measuresQuasiconvexification of geometric integralsHomogenization of variational problems in manifold valued Sobolev spacesCharacterization of generalized gradient Young measures generated by sequences in \(W^{1,1}\) and BVDimensional reduction for energies with linear growth involving the bending momentCharacterization of generalized Young measures generated by \({\mathcal{A}} \)-free measuresEuler's optimal profile problemOn the trace operator for functions of bounded \(\mathbb{A} \)-variationRelaxation of bulk and interfacial energiesOn a $\Gamma$-Limit of Willmore Functionals with Additional Curvature Penalization TermOn the relaxation of integral functionals depending on the symmetrized gradientOn the \(L^{1}\)-lower semicontinuity of certain convex functionals defined on \(BV\)-vector valued functionsThe affine Orlicz Pólya-Szegő principle on \(BV(\Omega )\)Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraintsA homogenization result in the gradient theory of phase transitionsOn the relaxation of some classes of dirichlet minimum problemsDislocation microstructures and strain-gradient plasticity with one active slip plane



Cites Work


This page was built for publication: On the relaxation in \(BV(\Omega ;\mathbb{R}^ m)\) of quasi-convex integrals