A local boundedness result for a class of obstacle problems with non-standard growth conditions

TL;DR

This paper establishes local boundedness of solutions to obstacle problems with non-standard growth, providing a sharp bound on the gap between growth exponents, advancing understanding of such problems.

Contribution

It introduces a new local boundedness result for obstacle problems with non-standard growth, under a precise condition on the growth exponents gap.

Findings

Proved local boundedness under sharp growth exponent bounds

Extended obstacle problem theory to non-standard growth conditions

Identified critical bounds for solution regularity

Abstract

We prove the local boundedness for solutions to a class of obstacle problems with non-standard growth conditions. The novelty here is that we are able to establish the local boundedness under a sharp bound on the gap between the growth exponents.