Lower semicontinuity and Young measures in BV without Alberti's Rank-One Theorem

DOI10.1515/acv.2011.008zbMath1239.49018arXiv1010.0242OpenAlexW2963828465MaRDI QIDQ2882720

Filip Rindler

Publication date: 7 May 2012

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.0242

zbMATH Keywords

differential inclusionrigiditylower semicontinuitybounded variationYoung measureAlberti's rank-one theorem

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Vector-valued set functions, measures and integrals (28B05) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Related Items (18)

On the singular part of measures constrained by linear PDEs and applications ⋮ Fine properties of functions of bounded deformation -- an approach via linear PDEs ⋮ A BV functional and its relaxation for joint motion estimation and image sequence recovery ⋮ Lower semicontinuity for an integral functional in BV ⋮ Piecewise affine approximations for functions of bounded variation ⋮ On the structure of \({\mathcal A}\)-free measures and applications ⋮ Lower semicontinuity and relaxation of signed functionals with linear growth in the context of \(\mathcal A\)-quasiconvexity ⋮ Homogenization problems in the calculus of variations: an overview ⋮ On the Structure of ∞-Harmonic Maps ⋮ Homogenization of functionals with linear growth in the context of \(\mathcal A\)-quasiconvexity ⋮ Existence for evolutionary problems with linear growth by stability methods ⋮ Generalized Multiscale Young Measures ⋮ Characterization of generalized Young measures generated by symmetric gradients ⋮ Directional oscillations, concentrations, and compensated compactness via microlocal compactness forms ⋮ Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures ⋮ A local proof for the characterization of Young measures generated by sequences in BV ⋮ Characterization of generalized Young measures generated by \({\mathcal{A}} \)-free measures ⋮ Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints

Cites Work

• Unnamed Item
• Oscillations and concentrations in weak solutions of the incompressible fluid equations
• Geometry of measures in \(R^ n:\) Distribution, rectifiability, and densities
• Relaxation of quasiconvex functionals in \(BV(\Omega, \mathbb{R}^ N)\) for integrands \(f(x, u, \bigtriangledown u)\)
• Relaxation of signed integral functionals in BV
• Characterization of generalized gradient Young measures generated by sequences in \(W^{1,1}\) and BV
• Fine phase mixtures as minimizers of energy
• On the relaxation in \(BV(\Omega ;\mathbb{R}^ m)\) of quasi-convex integrals
• Regularity of quasiconvex envelopes
• Quasi-Convex Integrands and Lower Semicontinuity in $L^1 $
• Quasiconvexification in W^1,1 and Optimal Jump Microstructure in BV Relaxation

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