Anal. Theory Appl., 31 (2015), pp. 381-393.
Published online: 2017-10
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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 $Γ$.
}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n4.4}, url = {http://global-sci.org/intro/article_detail/ata/4646.html} }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 $Γ$.