An elliptic boundary problem for a system involving a discontinuous weight

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2002
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Faierman, Melvin
Möller, Manfred
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Manuscripta mathematica. 2002, 108(3), pp. 289-317. Available under: doi: 10.1007/s002290200264
Zusammenfassung

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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510 Mathematik
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ISO 690DENK, Robert, Melvin FAIERMAN, Manfred MÖLLER, 2002. An elliptic boundary problem for a system involving a discontinuous weight. In: Manuscripta mathematica. 2002, 108(3), pp. 289-317. Available under: doi: 10.1007/s002290200264
BibTex
@article{Denk2002ellip-689,
  year={2002},
  doi={10.1007/s002290200264},
  title={An elliptic boundary problem for a system involving a discontinuous weight},
  number={3},
  volume={108},
  journal={Manuscripta mathematica},
  pages={289--317},
  author={Denk, Robert and Faierman, Melvin and Möller, Manfred}
}
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