The relaxed area of 𝕊1-valued singular maps in the strict BV-convergence

DOI10.1051/COCV/2022049zbMath1504.49030OpenAlexW4283827518WikidataQ114011430 ScholiaQ114011430MaRDI QIDQ5097303

Riccardo Scala, Simone Carano, Giovanni Bellettini

Publication date: 23 August 2022

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/cocv/2022049

zbMATH Keywords

relaxationarea functionalcartesian currents\(\mathbb{S}^1\)-valued singular mapstotal variation of the Jacobian

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Methods involving semicontinuity and convergence; relaxation (49J45) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75)

Related Items (1)

Relaxed area of graphs of piecewise Lipschitz maps in the strict \(BV\)-convergence

Cites Work

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• On the area of the graph of a singular map from the plane to the plane taking three values
• Weak notions of Jacobian determinant and relaxation
• Some properties of the degree for a class of Sobolev maps
• Functions of bounded higher variation
• Optimal estimates for the triple junction function and other surprising aspects of the area functional

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