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arXiv · 2203.15157

Sobolev spaces on arbitrary domains and semigroups generated by fractional Laplacian

Reinhard Farwig·Tsukasa Iwabuchi
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Abstract

We describe a procedure to introduce Sobolev spaces and the semigroup generated by the fractional Dirichlet Laplacian on an arbitrary domain of $\R^d$. In particular, the well-definedness of the spaces of both non-homogeneous and homogeneous type together with their duality properties, embeddings, and Gagliardo-Nirenberg inequalities will be discussed. We also show the continuity and the smoothing property of the semigroup.

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Reinhard Farwig, Tsukasa Iwabuchi. 2022-03-29. Sobolev spaces on arbitrary domains and semigroups generated by fractional Laplacian. https://arxiv.org/abs/2203.15157

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