H\"older continuity of the minimizer of an obstacle problem with generalized Orlicz growth

TL;DR

This paper establishes local H"older continuity and differentiability of solutions to obstacle problems with generalized Orlicz growth, encompassing various growth conditions like standard, variable exponent, and double phase.

Contribution

It provides new regularity results for obstacle problems with non-standard growth, extending known theories to more general Orlicz-type conditions.

Findings

Proves local $C^{0,eta}$-regularity of solutions.

Establishes local $C^{1,eta}$-regularity under certain conditions.

Results unify and extend regularity theory for multiple growth scenarios.

Abstract

We prove local $C^{0,\alpha}$- and $C^{1,\alpha}$-regularity for the local solution to an obstacle problem with non-standard growth. These results cover as special cases standard, variable exponent, double phase and Orlicz growth.