Year: 2015
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 4 : pp. 381–393
Abstract
Let $Γ ⊂ \mathbb{R}^2$ be a regular anisotropic fractal. We discuss the problem of the negative spectrum for the Schrödinger operators associated with the formal expression $$H_β =id−∆+βtr^Γ_b, β∈R,$$ acting in the anisotropic Sobolev space $W^{1,α}_2(\mathbb{R}^2)$, where $∆$ is the Dirichlet Laplanian in $\mathbb{R}^2$ and $tr^Γ_b$ is a fractal potential (distribution) supported by $Γ$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n4.4
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 4 : pp. 381–393
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Anisotropic function space anisotropic fractal Schrödinger operators negative eigenvalues.