Lipschitz regularity for a priori bounded minimizers of integral functionals with nonstandard growth

TL;DR

This paper proves that local minimizers of certain integral functionals with nonstandard growth conditions are Lipschitz continuous, under specific bounds relating growth and ellipticity exponents, advancing regularity theory in calculus of variations.

Contribution

It establishes Lipschitz regularity for a priori bounded minimizers with nonstandard growth, under sharp bounds on growth-ellipticity gap, improving understanding of regularity in complex variational problems.

Findings

Lipschitz regularity of minimizers proven under nonstandard growth conditions

Sharp bounds on growth-ellipticity gap are identified

Advances regularity results in calculus of variations with nonstandard growth

Abstract

We establish the Lipschitz regularity of the a priori bounded local minimizers of integral functionals with non autonomous energy densities satisfying non standard growth conditions under a sharp bound on the gap between the growth and the ellipticity exponent.