On the local everywhere bounndedness of the minima of a class of integral functionals of the Calculus of the Variations

TL;DR

This paper investigates the regularity and boundedness of minima for certain classes of integral functionals in the calculus of variations, providing insights into their local behavior and stability.

Contribution

It introduces new conditions ensuring local boundedness of minima for specific classes of variational functionals.

Findings

Minima are locally bounded under the proposed conditions.

The results extend previous regularity theorems.

Applications to broader classes of functionals are discussed.

Abstract

In this paper we study the regularity and the boundedness of the minima of two classes of functionals of the calculus of variations