Weakly smooth nonselfadjoint spectral elliptic boundary problems

Agranovič, Michail S.; Denk, Robert; Faierman, Melvin

Weakly smooth nonselfadjoint spectral elliptic boundary problems

Files

rd10.pdf(556.58 KB)

Date

1997

Authors

Agranovič, Michail S.

Denk, Robert

Faierman, Melvin

Publication type

Journal article

Published in

Mathematical topics ; 14 (1997). - pp. 138-199

Abstract

The paper is devoted to general elliptic boundary problems (A, B1 , ..., Bm) with a differential operator A of order 2m and general boundary conditions, acting in a bounded domain G of the n-dimensional space. No self-adjointness is assumed. The main goal is to minimize, to some extent, the smoothness assumptions under which the known spectral results are true. The main results concern the asymptotics of the trace of the q-th power of the resolvent, where q>n/2m, in an angle of ellipticity with parameter. For example, for the Dirichlet problem these asymptotics are obtained in the case of bounded and measurable coefficients in A and continuous coefficients in the principal part of A, while the boundary is assumed to belong to the Hölder space C2m-1,1. The asymptotics of the moduli of the eigenvalues are investigated. The last section is devoted to indefinite spectral problems, with a real-valued multiplier changing the sign in front of the spectral parameter.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

AGRANOVIČ, Michail S., Robert DENK, Melvin FAIERMAN, 1997. Weakly smooth nonselfadjoint spectral elliptic boundary problems. In: Mathematical topics. 14, pp. 138-199

BibTex

@article{Agranovic1997Weakl-606,
  year={1997},
  title={Weakly smooth nonselfadjoint spectral elliptic boundary problems},
  volume={14},
  journal={Mathematical topics},
  pages={138--199},
  author={Agranovič, Michail S. and Denk, Robert and Faierman, Melvin}
}

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