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

DOI10.1016/J.NA.2023.113424zbMath1530.49011arXiv2305.11299OpenAlexW4388028867MaRDI QIDQ6185361

Simone Carano, Riccardo Scala, Giovanni Bellettini

Publication date: 8 January 2024

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.11299

zbMATH Keywords

relaxationCartesian currentsarea functionalPlateau problemtotal variation of the Jacobianpiecewise Lipschitz mapsstrict BV convergence

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) 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) Length, area, volume, other geometric measure theory (28A75)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Graphs of finite mass which cannot be approximated in area by smooth graphs
• New lower semicontinuity results for polyconvex integrals
• On the relaxed total variation of singular maps
• On the total variation of the Jacobian.
• Strict convergence with equibounded area and minimal completely vertical liftings
• On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions
• Remarks on the total variation of the Jacobian
• 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
• Weak notions of Jacobian determinant and relaxation
• Strict convergence and minimal liftings in BV
• The relaxed area of 𝕊¹-valued singular maps in the strict BV-convergence
• Optimal estimates for the triple junction function and other surprising aspects of the area functional

This page was built for publication: Relaxed area of graphs of piecewise Lipschitz maps in the strict \(BV\)-convergence