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Sharp spectral asymptotics and Weyl formula for elliptic operators with Non-smooth Coefficients-Part 2

Lech Zielinski — 2002

Colloquium Mathematicae

We describe the asymptotic distribution of eigenvalues of self-adjoint elliptic differential operators, assuming that the first-order derivatives of the coefficients are Lipschitz continuous. We consider the asymptotic formula of Hörmander's type for the spectral function of pseudodifferential operators obtained via a regularization procedure of non-smooth coefficients.

Semiclassical distribution of eigenvalues for elliptic operators with Hölder continuous coefficients, part i: non-critical case

Lech Zieliński — 2004

Colloquium Mathematicae

We consider a version of the Weyl formula describing the asymptotic behaviour of the counting function of eigenvalues in the semiclassical approximation for self-adjoint elliptic differential operators under weak regularity hypotheses. Our aim is to treat Hölder continuous coefficients and to investigate the case of critical energy values as well.

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