An elliptic boundary problem for a system involving a discontinuous weight | Zendy

Robert Denk | Zendy; M. Faierman | Zendy; Manfred Möller | Zendy

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An elliptic boundary problem for a system involving a discontinuous weight

Author(s) -

Robert Denk,

M. Faierman,

Manfred Möller

Publication year - 2002

Publication title -

manuscripta mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.752

H-Index - 46

eISSN - 1432-1785

pISSN - 0025-2611

DOI - 10.1007/s002290200264

Subject(s) - mathematics , eigenvalues and eigenvectors , counterexample , scalar (mathematics) , a priori and a posteriori , boundary (topology) , jacobian matrix and determinant , diagonal , mathematical analysis , number theory , algebraic geometry , completeness (order theory) , elliptic curve , pure mathematics , discrete mathematics , geometry , philosophy , physics , epistemology , quantum mechanics

In a recent paper, Agranovich, Denk and Faierman dealt with a priori estimates, completeness, Abel-Lidskii summability, and eigenvalue asymptotics for scalar elliptic boundary eigenvalue problems involving discontinuous weights. Here we extend these results to the matrix valued case with a diagonal discontinuous weight matrix. The given region is subdivided into subregions on which the weights are continuous. Whereas in the scalar case the usual ellipticity conditions suffice to obtain a priori estimates, a counterexample shows that here transmission conditions at the boundaries of the subregions are also needed.

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