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Boundary value problems for a class of elliptic operator pencils

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Abstract

In this paper operator pencilsA(x, D, λ) 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 the 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 is proved for the Dirichlet boundary value problem connected with an N-elliptic pencil.

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Authors and Affiliations

  1. NWF I-Mathematik, Universität Regensburg, D-93040, Regensburg, Germany

    R. Denk & R. Mennicken

  2. Keldysh Institute of Applied Mathematics, Russian Acad. Sci., Miusskaya sqr. 4, 125047, Moscow, Russia

    L. Volevich

Authors
  1. R. Denk
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  2. R. Mennicken
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  3. L. Volevich
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Supported in part by the Deutsche Forschungsgemeinschaft and by Russian Foundation of Fundamental Research, Grant 00-01-00387.

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Denk, R., Mennicken, R. & Volevich, L. Boundary value problems for a class of elliptic operator pencils. Integr equ oper theory 38, 410–436 (2000). https://doi.org/10.1007/BF01228606

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  • DOI: https://doi.org/10.1007/BF01228606

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