An elementary proof of the rank-one theorem for BV functions

DOI10.4171/JEMS/903zbMath1426.26028arXiv1601.02903OpenAlexW2964321877MaRDI QIDQ2327714

Davide Vittone, Annalisa Massaccesi

Publication date: 15 October 2019

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.02903

zbMATH Keywords

functions of bounded variationrank-one theorem

Mathematics Subject Classification ID

Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Related Items (12)

Fine properties of functions of bounded deformation -- an approach via linear PDEs ⋮ BV spaces and the perimeters related to Schrödinger operators with inverse-square potentials and applications to the rank-one theorem ⋮ A-free measures and applications ⋮ Subgraphs of \(\alpha\)-Hermite BV functions and the rank-one theorem for \(\mathcal{BV}_{\mathcal{H}_{\alpha}}\) ⋮ Subgraphs of BV functions on RCD spaces ⋮ Characterization of generalized Young measures generated by symmetric gradients ⋮ Dimensional estimates and rectifiability for measures satisfying linear PDE constraints ⋮ On a $\Gamma$-Limit of Willmore Functionals with Additional Curvature Penalization Term ⋮ On the relaxation of integral functionals depending on the symmetrized gradient ⋮ Fine properties of functions with bounded variation in Carnot-Carathéodory spaces ⋮ The four-state problem and convex integration for linear differential operators ⋮ Differentiability in measure of the flow associated with a nearly incompressible BV vector field

Cites Work

• On the structure of \({\mathcal A}\)-free measures and applications
• Rank-one theorem and subgraphs of BV functions in Carnot groups
• Rank one property for derivatives of functions with bounded variation
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