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arXiv · 2211.05511

The fractional Laplacian with reflections

Krzysztof Bogdan·Markus Kunze
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Abstract

Motivated by the notion of isotropic $\alpha$-stable L\'evy processes confined, by reflections, to a bounded open Lipschitz set $D\subset \mathbb{R}^d$, we study some related analytical objects. Thus, we construct the corresponding transition semigroup, identify its generator and prove exponential speed of convergence of the semigroup to a unique stationary distribution for large time.

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Krzysztof Bogdan, Markus Kunze. 2022-11-10. The fractional Laplacian with reflections. https://arxiv.org/abs/2211.05511

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