Parameter-elliptic boundary value problems connected with the Newton polygon

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2002
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Volevič, Leonid R.
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Differential and Integral Equations. 2002, 15(3), pp. 289-326
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In this paper pencils of partial differential operators depending polynomially on a complex parameter and corresponding boundary value problems with general boundary conditions are studied. We define a concept of ellipticity for such problems (for which the parameter-dependent symbol in general is not quasi-homogeneous) in terms of the Newton polygon and introduce related parameter-dependent norms. It is shown that this type of ellipticity leads to unique solvability of the boundary value problem and to two-sided a priori estimates for the solution.

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510 Mathematik
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ISO 690DENK, Robert, Leonid R. VOLEVIČ, 2002. Parameter-elliptic boundary value problems connected with the Newton polygon. In: Differential and Integral Equations. 2002, 15(3), pp. 289-326
BibTex
@article{Denk2002Param-511,
  year={2002},
  title={Parameter-elliptic boundary value problems connected with the Newton polygon},
  number={3},
  volume={15},
  journal={Differential and Integral Equations},
  pages={289--326},
  author={Denk, Robert and Volevič, Leonid R.}
}
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