Eigenvalue distribution of some fractal semi-elliptic differential operators
نویسندگان
چکیده
We consider differential operators of type Au(x) = u(x) + (−1)t1 ∂ 2t1u(x) ∂x1 1 + (−1)t2 ∂ 2t2u(x) ∂x2 2 , x = (x1, x2) ∈ R2, and Sierpinski carpets Γ ⊂ R2. The aim of the paper is to investigate spectral properties of the fractal differential operator A−1 ◦ trΓ acting in the anisotropic Sobolev space W (t1,t2) 2 (R 2) where trΓ is closely related to the trace operator trΓ . Mathematics Subject Classification (1991): 35P15, 46E35, 28A90
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