TY - JOUR

T1 - Spectrum asymptotics for one “nonsmooth” variational problem with solvable constraint

AU - Alekseev, A. B.

AU - Birman, M. Sh

AU - Filonov, N. D.

PY - 2007/1/1

Y1 - 2007/1/1

N2 - In a previous paper by Birman and Filonov, the spectrum of the Maxwell operator with nonsmooth coefficients in Lipschitz domains was investigated. The claim that its eigenvalues obey the Weyl asymptotics was proved up to a statement about the spectrum of an auxiliary problem with constraint. The proof of that statement is given in the present paper.

AB - In a previous paper by Birman and Filonov, the spectrum of the Maxwell operator with nonsmooth coefficients in Lipschitz domains was investigated. The claim that its eigenvalues obey the Weyl asymptotics was proved up to a statement about the spectrum of an auxiliary problem with constraint. The proof of that statement is given in the present paper.

KW - Problem with constraint

KW - Resonator with perfectly conductive boundary

KW - Spectrum of the quotient of quadratic forms

KW - Weyl spectrum asymptotics

UR - http://www.scopus.com/inward/record.url?scp=85009773788&partnerID=8YFLogxK

U2 - 10.1090/S1061-0022-07-00968-5

DO - 10.1090/S1061-0022-07-00968-5

M3 - статья

AN - SCOPUS:85009773788

VL - 18

SP - 681

EP - 697

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -