Local boundedness of minimizers under unbalanced Orlicz growth conditions

TL;DR

This paper investigates the local boundedness of minimizers for variational integral functionals with non-standard growth conditions, extending classical results to more general unbalanced Orlicz growth scenarios.

Contribution

It establishes local boundedness of minimizers under unbalanced Orlicz growth conditions, including classical and quasi-minimizers, generalizing existing results for p,q-growth functionals.

Findings

Local boundedness of minimizers under unbalanced Orlicz growth.

Extension of classical p,q-growth results to more general growth conditions.

Inclusion of quasi-minimizers in the boundedness analysis.

Abstract

Local minimizers of integral functionals of the calculus of variations are analyzed under growth conditions dictated by different lower and upper bounds for the integrand. Growths of non-necessarily power type are allowed. The local boundedness of the relevant minimizers is established under a suitable balance between the lower and the upper bounds. Classical minimizers, as well as quasi-minimizers are included in our discussion. Functionals subject to so-called $p,q$-growth conditions are embraced as special cases and the corresponding sharp results available in the literature are recovered.