Manifold-constrained free discontinuity problems and Sobolev approximation

2023/07/05 by Federico Luigi Dipasquale, Bianca Stroffolini, Dipasquale, Federico Luigi +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2307.02265

openalex publication_date 2023/07/05 · openalex created_date 2023/07/07 · openalex updated_date 2026/07/28

Abstract

We study the regularity of local minimisers of a prototypical free-discontinuity problem involving both a manifold-valued constraint on the maps (which are defined on a bounded domain Ω⊂ \R²) and a variable-exponent growth in the energy functional. To this purpose, we first extend to this setting the Sobolev approximation result for special function of bounded variation with small jump set originally proved by Conti, Focardi, and Iurlano \citeCFI-ARMA, CFI-AIHP for special functions of bounded deformation. Secondly, we use this extension to prove regularity of local minimisers.

Related

• Regularity of minimizers for free-discontinuity problems with p(⋅)-growth
• Strong existence for free-discontinuity problems with non-standard growth
• On De Giorgi's Conjecture of Nonlocal approximations for free-discontinuity problems: The symmetric gradient case
• Constraint maps with free boundaries: the Bernoulli case
• Manifold constrained non-uniformly elliptic problems