Denk, Robert and Mennicken, Reinhard and Volevich, Leonid (1998) The Newton polygon and elliptic problems with parameter. MATHEMATISCHE NACHRICHTEN, 192 (1). pp. 125-157. ISSN 0025-584X, 1522-2616
Full text not available from this repository.Abstract
In the study of the resolvent of a scalar elliptic operator, say, on a manifold without boundary there is a well-known Agmon-Agranovich-Vishik condition of ellipticity with parameter which guarantees the existence of a ray of minimal growth of the resolvent. The paper is devoted to the investigation of the same problem in the case of systems which are elliptic in the sense of Douglis-Nirenberg. We look for algebraic conditions on the symbol providing the existence of the resolvent set containing a ray on the complex plane. We approach the problem using the Newton polyhedron method. The idea of the method is to study simultaneously all the quasihomogeneous parts of the system obtained by assigning to the spectral parameter various weights, defined by the corresponding Newton polygon. On this way several equivalent necessary and sufficient conditions on the symbol of the system guaranteeing the existence and sharp estimates for the resolvent are found. One of the equivalent conditions can be formulated in the following form: all the upper left miners of the symbol satisfy ellipticity conditions. This subclass of systems elliptic in the sense of Douglis-Nirenberg was introduced by A. KOZHEVNIKOV [K2].
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Newton polygon; systems elliptic in the sense of Douglis-Nirenberg; systems elliptic with parameter |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 01 Mar 2023 09:34 |
| Last Modified: | 01 Mar 2023 09:34 |
| URI: | https://pred.uni-regensburg.de/id/eprint/50258 |
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