On the local everywhere H\"older continuity for weak solutions of a class of not convex vectorial problems of the Calculus of Variations

TL;DR

This paper investigates the regularity of local minima for a class of vectorial calculus of variations problems, focusing on local H"older continuity without assuming convexity or specific structural conditions on the density.

Contribution

It establishes local H"older continuity of solutions for non-convex variational problems without structural or radial assumptions on the density.

Findings

Proves local H"older continuity for weak solutions

Applies to non-convex, quasi-convex, policonvex, and rank-one convex densities

Does not require structure, radial, or diagonal assumptions

Abstract

In this paper we study the regularity of the local minima of integral functionals: in particular, not convexity (quasi-convexity, policonvexity or rank one convexity) hypothesis will be made on the density, neither structure hypothesis nor radial nor diagonal.