Bounded minimizers of double phase problems at nearly linear growth

TL;DR

This paper investigates the regularity of bounded minimizers in double phase problems with nearly linear growth, establishing local Hölder continuity of the gradient under specific nonuniformity conditions.

Contribution

It introduces new regularity results for minimizers of double phase problems at nearly linear growth, expanding understanding of their gradient behavior.

Findings

Gradient of minimizers is locally Hölder continuous.

Regularity holds within the sharp maximal nonuniformity range.

Results apply to problems with nearly linear growth conditions.

Abstract

Bounded minimizers of double phase problems at nearly linear growth have locally H\"older continuous gradient within the sharp maximal nonuniformity range $q<1+\alpha$.