Publikation:

On elliptic operator pencils with general boundary conditions

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2001

Autor:innen

Mennicken, Reinhard
Volevič, Leonid R.

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http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-50693
DOI (zitierfähiger Link)
https://doi.org/10.1007/BF01192148
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Attribution-NonCommercial-NoDerivs 2.0 Generic

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Published

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Integral equations and operator theory. 2001, 39(1), pp. 15-40. Available under: doi: 10.1007/BF01192148

Zusammenfassung

In this paper parameter-dependent partial differential operators are investigated which satisfy the condition of N-ellipticity with parameter, an ellipticity condition formulated with the use of the Newton polygon. For boundary value problems with general boundary operators we define N-ellipticity including an analogue of the Shapiro Lopatinskii condition. It is shown that the boundary value problem is N-elliptic if and only if an a priori estimate with respect to certain parameter-dependent norms holds. These results are closely connected with singular perturbation theory and lead to uniform estimates for problems of Vishik Lyusternik type containing a small parameter.

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510 Mathematik

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ISO 690DENK, Robert, Reinhard MENNICKEN, Leonid R. VOLEVIČ, 2001. On elliptic operator pencils with general boundary conditions. In: Integral equations and operator theory. 2001, 39(1), pp. 15-40. Available under: doi: 10.1007/BF01192148
BibTex
@article{Denk2001ellip-681,
  year={2001},
  doi={10.1007/BF01192148},
  title={On elliptic operator pencils with general boundary conditions},
  number={1},
  volume={39},
  journal={Integral equations and operator theory},
  pages={15--40},
  author={Denk, Robert and Mennicken, Reinhard and Volevič, Leonid R.}
}
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