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Boundary value problems for a class of elliptic operator pencils

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2000

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Mennicken, Reinhard
Volevič, Leonid R.

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http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-50716
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https://doi.org/10.1007/BF01228606
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Attribution-NonCommercial-NoDerivs 2.0 Generic

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Integral Equations Operator Theory. 2000, 38, pp. 410-436. Available under: doi: 10.1007/BF01228606

Zusammenfassung

An operator family of densely defined closed linear operators and the In this paper operator pencils depending polynomially on the spectral parameter are studied which act on a manifold with boundary and satisfy the condition of N -ellipticity with parameter, a generalization of the notion of ellipticity with parameter as introduced by Agmon and Agranovich-Vishik. Sobolev spaces corresponding to a Newton polygon are defined and investigated; in particular it is possible to describe their trace spaces. With respect to these spaces, an a priori estimate holds for the Dirichlet boundary value problem connected with an N-elliptic pencil, and a right parametrix is constructed.

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510 Mathematik

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ISO 690DENK, Robert, Reinhard MENNICKEN, Leonid R. VOLEVIČ, 2000. Boundary value problems for a class of elliptic operator pencils. In: Integral Equations Operator Theory. 2000, 38, pp. 410-436. Available under: doi: 10.1007/BF01228606
BibTex
@article{Denk2000Bound-704,
  year={2000},
  doi={10.1007/BF01228606},
  title={Boundary value problems for a class of elliptic operator pencils},
  volume={38},
  journal={Integral Equations Operator Theory},
  pages={410--436},
  author={Denk, Robert and Mennicken, Reinhard and Volevič, Leonid R.}
}
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    <dcterms:abstract xml:lang="eng">An operator family of densely defined closed linear operators and the In this paper operator pencils depending polynomially on the spectral parameter  are studied which act on a manifold with boundary and satisfy the condition of  N -ellipticity with parameter, a generalization of the notion of ellipticity with parameter as introduced by Agmon and Agranovich-Vishik. Sobolev spaces corresponding to a Newton polygon are defined and investigated; in particular it is possible to describe  their trace spaces. With respect to these spaces, an a priori estimate  holds for the Dirichlet boundary value problem connected with an N-elliptic pencil, and a right parametrix is constructed.</dcterms:abstract>
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