(untitled) (Analysis in Theory and Applications, 2017)
Let Γ ⊂ 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(R^2), where ∆ is the Dirichlet Laplanian in R^2 and tr^Γ_b is a fractal potential (distribution) supported by Γ.