Singular orthotropic functionals with nonstandard growth conditions

TL;DR

This paper investigates a convex orthotropic functional with nonstandard growth, establishing local Lipschitz continuity and higher differentiability of bounded local minimizers without growth ratio restrictions.

Contribution

It proves regularity and higher differentiability of minimizers for a nonstandard growth convex functional with orthotropic structure, including non-autonomous lower order terms.

Findings

Bounded local minimizers are locally Lipschitz.

No restriction on growth rate ratios is needed.

Higher differentiability of minimizers is established.

Abstract

We pursue the study of a model convex functional with orthotropic structure and nonstandard growth conditions, this time focusing on the sub-quadratic case. We prove that bounded local minimizers are locally Lipschitz. No restriction on the ratio between the highest and the lowest growth rates are needed. The result holds also in presence of a non-autonomous lower order term, under sharp integrability assumptions. Finally, we prove higher differentiability of bounded local minimizers, as well.