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.
On fractional Laplacians -- 2
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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 $s\in(-1,0)$.
fields
math.AP 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
The Lewy-Stampacchia Inequality for the Fractional Laplacian and Its Application to Anomalous Unidirectional Diffusion Equations
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.