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arXiv · 2606.08559

Strong comparison principle and symmetry results for the fractional $p$-Laplacian

Anup Biswas·Subhajit Roy·Aniket Sen
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Abstract

In this article, we study the equation $$ (-\Delta_p)^s u = f(u) $$ in a bounded domain $\Omega\subset \mathbb{R}^n$, where $n\geq 2$, $p>2$, and $f$ is locally Lipschitz. We establish a strong comparison principle in a fairly general setting and use it to derive symmetry results for positive $C^1$ solutions satisfying Dirichlet boundary conditions. We also show that the $C^1$ regularity assumption is indeed satisfied for $p\in \left[2,\frac{2}{1-s}\right)$.

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Anup Biswas, Subhajit Roy, Aniket Sen. 2026-06-07. Strong comparison principle and symmetry results for the fractional $p$-Laplacian. https://arxiv.org/abs/2606.08559

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