Higher Hölder regularity for fractional $(p,q)$-Laplace equations

Abstract

We study the fractional $(p,q)$-Laplace equation $$(-\hat{I}{”}_p{)}^{s}u+(-\hat{I}{”}_q{)}^{t}u=0$$ for $s,t\in (0,1)$ and $p,q\in (1,\infty )$. We establish Hölder estimates with an explicit exponent. As a consequence, we derive a Liouville-type theorem. Our approach builds on techniques previously developed for the fractional $p$-Laplace equation, relying on a Moser-type iteration for difference quotients.