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On a fractional boundary version of Talenti's inequality in the unit ball https://arxiv.org/abs/2411.14534 #mathAP

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

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 $(-Δ)^s$ in the unit ball $Ω= B_1(0) \subset \mathbb{R}^N$. 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.

arXiv.org
November 26, 2024 at 3:10 AM · · feed2toot · 0 · 0 · 0
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