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Displaying similar documents to “Semiclassical distribution of eigenvalues for elliptic operators with Hölder continuous coefficients, part i: non-critical case”

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

Lech Zielinski (2002)

Colloquium Mathematicae

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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.

Two remarks about spectral asymptotics of pseudodifferential operators

Wojciech Czaja, Ziemowit Rzeszotnik (1999)

Colloquium Mathematicae

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In this paper we show an asymptotic formula for the number of eigenvalues of a pseudodifferential operator. As a corollary we obtain a generalization of the result by Shubin and Tulovskiĭ about the Weyl asymptotic formula. We also consider a version of the Weyl formula for the quasi-classical asymptotics.

A characterization of elliptic operators

Grzegorz Łysik, Paweł M. Wójcicki (2014)

Annales Polonici Mathematici

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We give a characterization of constant coefficients elliptic operators in terms of estimates of their iterations on smooth functions.

On Dittmar's approach to the Beltrami equation

Ewa Ligocka (2002)

Colloquium Mathematicae

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We recall an old result of B. Dittmar. This result permits us to obtain an existence theorem for the Beltrami equation and some other results as a direct consequence of Moser's classical estimates for elliptic operators.

On elliptic systems pertaining to the Schrödinger equation

J. Chabrowski, E. Tonkes (2003)

Annales Polonici Mathematici

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We discuss the existence of solutions for a system of elliptic equations involving a coupling nonlinearity containing a critical and subcritical Sobolev exponent. We establish the existence of ground state solutions. The concentration of solutions is also established as a parameter λ becomes large.