摘要
Let Γ?R;be a regular anisotropic fractal. We discuss the problem of the negative spectrum for the Schr?dinger operators associated with the formal expression H;=id-?+βtr;,β∈R,acting in the anisotropic Sobolev space W;（R;）, where ? is the Dirichlet Laplanian in R;and tr;is a fractal potential（distribution） supported by Γ.
Let Γ?R^2 be a regular anisotropic fractal. We discuss the problem of the negative spectrum for the Schr?dinger operators associated with the formal expression H_β=id-?+βtr_b~Γ,β∈R,acting in the anisotropic Sobolev space W_2^(1,α)(R^2), where ? is the Dirichlet Laplanian in R^2 and tr_b~Γ is a fractal potential(distribution) supported by Γ.
基金
supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.13KJB110010)
the Pre Study Foundation of Nanjing University of Finance&Economics(Grant No.YYJ2013016)
the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)
