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arXiv · 2411.14534

On a fractional boundary version of Talenti's inequality in the unit ball

Yassin El Karrouchi·Tobias Weth
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Abstract

Inspired by recent work of Ferone and Volzone arXiv:2007.13195, we derive sufficient conditions for the validity and non-validity of a boundary version of Talenti's comparison principle in the context of Dirichlet-Poisson problems for the fractional Laplacian $(-\Delta)^s$ in the unit ball $\Omega= B_1(0) \subset \mathbb{R}^N$. In particular, our results imply a universial failure of the classical pointwise Talenti inequality in the fractional radial context which sheds new light on the one-dimensional counterexamples given in arXiv:2007.13195.

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Yassin El Karrouchi, Tobias Weth. 2024-11-21. On a fractional boundary version of Talenti's inequality in the unit ball. https://doi.org/10.1016/j.nonrwa.2025.104482

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