On the local everywhere H\"older continuity of the minima of a class of vectorial integral functionals of the calculus of variations

TL;DR

This paper investigates the conditions under which the minimizers of certain vectorial integral functionals exhibit everywhere H"older continuity, contributing to the regularity theory in the calculus of variations.

Contribution

It establishes new regularity results ensuring the H"older continuity of minimizers for a broad class of vectorial integral functionals.

Findings

Minimizers are everywhere H"older continuous under specified conditions.

The results extend previous regularity theorems to more general functional classes.

The paper provides a framework for analyzing regularity in vectorial variational problems.

Abstract

In this paper we study the everywhere H\"oder continuity of the minima of a class of vectorial integral funcionals