Higher H\"older regularity for fractional $(p,q)$-Laplace equations

Abstract

We study the fractional $(p,q)$-Laplace equation $$ (-\Delta_p)^s u +(-\Delta_q)^t u= 0 $$ for $s,t\in(0,1)$ and $p,q\in(1,\infty)$. We establish H\"older 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.