On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions

DOI10.1007/S10231-019-00887-0zbMath1436.49053arXiv1901.01781OpenAlexW2958537160WikidataQ127590933 ScholiaQ127590933MaRDI QIDQ2309433

Giovanni Bellettini, Riccardo Scala, Alaa Elshorbagy, Maurizio Paolini

Publication date: 1 April 2020

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

Full work available at URL: https://arxiv.org/abs/1901.01781

zbMATH Keywords

relaxationminimal surfacesCartesian currentsarea functionalPlateau problem

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) 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 (2)

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

Cites Work

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• Semicartesian surfaces and the relaxed area of maps from the plane to the plane with a line discontinuity
• Integral representation on \(BV(\Omega )\) of \(\Gamma\)-limits of variational integrals
• New lower semicontinuity results for polyconvex integrals
• A direct proof for lower semicontinuity of polyconvex functionals
• 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
• Optimal estimates for the triple junction function and other surprising aspects of the area functional

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