Relaxation of quasi-convex functionals with variable exponent growth
Analysis of PDEs
2026-01-21 v3 Functional Analysis
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.
Cite
@article{arxiv.2510.04672,
title = {Relaxation of quasi-convex functionals with variable exponent growth},
author = {Giacomo Bertazzoni and Petteri Harjulehto and Peter Hästö and Elvira Zappale},
journal= {arXiv preprint arXiv:2510.04672},
year = {2026}
}