Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth

2023/01/18 by Stefano Almi, Almi, Stefano, Dario Reggiani +3 · 1 citation
Computer Science · Mathematics · #46E30 #49J45 #49M20 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.07406

openalex publication_date 2023/01/18 · openalex created_date 2023/01/20 · openalex updated_date 2026/08/01

Abstract

A lower semicontinuity result and a relaxation formula for free discontinuity functionals with non-standard growth in the bulk energy are provided. Our analysis is based on a non-trivial adaptation of the blow-up (Ambrosio 1994) and of the global method for relaxation (Bouchitté et al. 1998) to the setting of generalized special function of bounded variation with Orlicz growth. Key tools developed in this paper are an integral representation result and a Poincaré inequality under non-standard growth.

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