On the regularity of the $\omega$-minima of $\varphi$-functionals

TL;DR

This paper investigates the regularity of $ ext{omega}$-minima in variational integrals with $ ext{phi}$-growth, providing bounds on the Hausdorff dimension of their singular sets.

Contribution

It offers new insights into the regularity properties of $ ext{omega}$-minima and establishes an upper bound on the Hausdorff dimension of their singularities.

Findings

Established an upper bound on the Hausdorff dimension of the singular set.

Analyzed regularity properties of $ ext{omega}$-minima with $ ext{phi}$-growth.

Contributed to the understanding of singularities in variational problems.

Abstract

We focus on some regularity properties of $\omega$-minima of variational integrals with $\varphi$-growth and we provide an upper bound on the Hausdorff dimension of their singular set.