On fractional Laplacians -- 2

Alexander I. Nazarov; Roberta Musina

On fractional Laplacians -- 2

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arxiv 1408.3568 v2 pith:BP2LXB76 submitted 2014-08-15 math.AP

Roberta Musina , Alexander I. Nazarov This is my paper · ORCID

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keywords fractionallaplaciansnaturalarxivcaffarelli--silvestrecharacterizationscomparedelta

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abstract

The present paper is the natural evolution of arXiv:1308.3606. For $s>-1$ we compare two natural types of fractional Laplacians $(-\Delta)^s$, namely, the "Navier" and the "Dirichlet" ones. As a main tool, we give the "dual" Caffarelli--Silvestre and Stinga--Torrea variational characterizations of these operators for $s\in(-1,0)$.

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The Lewy-Stampacchia Inequality for the Fractional Laplacian and Its Application to Anomalous Unidirectional Diffusion Equations
math.AP 2019-09 conditional novelty 6.0 of 10

For the spectral fractional Laplacian on a bounded domain, obstacle solutions satisfy the Lewy-Stampacchia inequality f ≤ Au ≤ max{f, Aψ}, which yields well-posedness of a fractional unidirectional diffusion equation.

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