Relaxation of quasi-convex functionals with variable exponent growth

2025/10/06 by Giacomo Bertazzoni, Petteri Harjulehto, Bertazzoni, Giacomo +5
Computer Science · Mathematics · #26A45 #26B30 #46E35 #46E99 #49J45 #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2510.04672

openalex publication_date 2025/10/06 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

Abstract

We prove a relaxation result for a quasi-convex bulk integral functional with variable exponent growth in a suitable space of bounded variation type. A key tool is a decomposition under mild assumptions of the energy into absolutely continuous and singular parts weighted via a recession function.

Citations

• Asymptotic analysis of thin structures with point dependent energy growth
• Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth
• An optimal design problem with non-standard growth and no concentration effects
• Relaxation for an optimal design problem with nonstandard growth
• -convergence of power-law functionals with variable exponents

Cited by

• Functions of bounded Musielak-Orlicz-type deformation and anisotropic Total Generalized Variation for image-denoising problems

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