Variational inequalities for the spectral fractional Laplacian

Alexander I. Nazarov; Roberta Musina

Variational inequalities for the spectral fractional Laplacian

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arxiv 1603.05730 v1 pith:T2N2RNP5 submitted 2016-03-17 math.AP

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

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keywords fractionallaplacianomegaspectralboundeddeltadomaininequalities

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abstract

In this paper we study the obstacle problems for the Navier (spectral) fractional Laplacian $\left(-\Delta_\Omega\right)^{\!s}$ of order $s\in(0,1)$, in a bounded domain $\Omega\subset\mathbb R^n$.

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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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