# Global continuity and higher integrability of a minimizer of an obstacle problem under generalized Orlicz growth conditions

## TL;DR

This paper proves boundary continuity and higher gradient integrability for minimizers of obstacle problems under generalized Orlicz growth, extending known results and introducing new findings for Orlicz and double phase growth conditions.

## Contribution

It establishes boundary continuity and higher integrability of minimizers under generalized Orlicz growth, generalizing previous results and providing new insights for Orlicz and double phase growth.

## Key findings

- Proves boundary continuity of minimizers.
- Establishes higher integrability of gradients.
- Extends results to Orlicz and double phase growth cases.

## Abstract

We prove continuity up to the boundary of the minimizer of an obstacle problem and higher integrability of its gradient under generalized Orlicz growth. The result recovers similar results obtained in the special cases of polynomial growth, variable exponent growth and produces new results for Orlicz and double phase growth.