Local Lipschitz continuity for energy integrals with slow growth and lower order terms

TL;DR

This paper proves that local minimizers of certain energy functionals with slow growth and lower order terms are locally Lipschitz continuous, using recent results on Bounded Slope Conditions, with applications in elastoplastic torsion and image restoration.

Contribution

It establishes local Lipschitz regularity for minimizers of energy integrals with slow growth and explicit lower order dependence, extending previous regularity results.

Findings

Local minimizers are locally Lipschitz continuous.

Applicable to elastoplastic torsion and image restoration problems.

Uses recent Bounded Slope Conditions results.

Abstract

We consider integral functionals with slow growth and explicit dependence on u of the lagrangian; this includes many relevant examples, as, for instance, in elastoplastic torsion problems or in image restoration problems. Our aim is to prove that the local minimizers are locally Lipschitz continuous. The proof makes use of recent results concerning the Bounded Slope Conditions.