JournalszaaVol. 28, No. 2pp. 233–248

Eigenvalue Distribution of Semi-Elliptic Operators in Anisotropic Sobolev Spaces

  • Erika Tamási

    Sapientia University, Cluj-Napoca, Romania
Eigenvalue Distribution of Semi-Elliptic Operators in Anisotropic Sobolev Spaces cover
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Abstract

We study the spectral properties of the compact non-negative self-adjoint operator T=A−1∘trΓT=A^{-1}\circ \mathrm{tr}^\Gamma acting in the anisotropic Sobolev space H2s,a(\rn)H^{s,a}_2(\rn) and give two-sided estimates for the asymptotic behaviour of its eigenvalues λk(T)\lambda_k(T), where AA is a semi-elliptic differential operator of type

Au(x)=(−1)s1∂2s1u(x)∂x12s1+⋯+(−1)sn∂2snu(x)∂xn2sn+u(x),Au(x)=(-1)^{s_1}\frac{\partial^{2s_1}u(x)}{\partial x_1^{2s_1}} + \cdots + (-1)^{s_n}\frac{\partial^{2s_n}u(x)}{\partial x_n^{2s_n}} + u(x),

and trΓ\mathrm{tr}^{\Gamma} a special trace operator on an anisotropic dd-set Γ\Gamma.

Cite this article

Erika Tamási, Eigenvalue Distribution of Semi-Elliptic Operators in Anisotropic Sobolev Spaces. Z. Anal. Anwend. 28 (2009), no. 2, pp. 233–248

DOI 10.4171/ZAA/1383