Partial Regularity Results for Asymptotic Quasiconvex Functionals with General Growth

TL;DR

This paper establishes partial regularity for minimizers of vectorial integrals with general growth, under asymptotic quasiconvexity conditions, advancing understanding in the calculus of variations.

Contribution

It introduces a novel approach to partial regularity for functionals with general growth, relying on asymptotic quasiconvexity assumptions.

Findings

Proves partial regularity of minimizers under new conditions

Extends regularity results to broader class of functionals

Provides techniques applicable to calculus of variations problems

Abstract

We prove partial regularity for minimizers of vectorial integrals of the Calculus of Variations, with general growth condition, imposing quasiconvexity assumptions only in an asymptotic sense.