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arXiv · 2509.15988

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

Prashanta Garain·Erik Lindgren
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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.

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Prashanta Garain, Erik Lindgren. 2025-09-19. Higher H\"older regularity for fractional $(p,q)$-Laplace equations. https://arxiv.org/abs/2509.15988

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