Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity

DOI10.1007/s10231-016-0556-9zbMath1352.49007OpenAlexW1787975113MaRDI QIDQ343510

Giovanni Bellettini, Lucia Tealdi, Maurizio Paolini

Publication date: 28 November 2016

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-016-0556-9

zbMATH Keywords

graph arearelaxed area functionalsemi-Cartesian surfaces

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Geometric measure and integration theory, integral and normal currents in optimization (49Q15)

Related Items (3)

The relaxed area of 𝕊¹-valued singular maps in the strict BV-convergence ⋮ Relaxed area of graphs of piecewise Lipschitz maps in the strict \(BV\)-convergence ⋮ On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions

Cites Work

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• Integral representation on \(BV(\Omega )\) of \(\Gamma\)-limits of variational integrals
• New lower semicontinuity results for polyconvex integrals
• Sublinear functions of measures and variational integrals
• On the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity
• On the area of the graph of a singular map from the plane to the plane taking three values
• Minimal Surfaces
• Direct methods in the calculus of variations

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