Local H\"older continuity for fractional nonlocal equations with general growth

TL;DR

This paper establishes local boundedness and H"older continuity of solutions to generalized fractional p-Laplacian equations using a fractional Sobolev-Poincaré inequality.

Contribution

It introduces new regularity results for nonlocal equations with general growth conditions, expanding understanding of solution behavior.

Findings

Proved local boundedness of weak solutions.

Established H"older continuity under broad conditions.

Developed a fractional Sobolev-Poincaré inequality for these equations.

Abstract

We study generalized fractional $p$-Laplacian equations to prove local boundedness and H\"older continuity of weak solutions to such nonlocal problems by finding a suitable fractional Sobolev-Poincar\'e inquality.