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2002 Parameter-elliptic boundary value problems connected with the Newton polygon
Robert Denk, Leonid Volevich
Differential Integral Equations 15(3): 289-326 (2002). DOI: 10.57262/die/1356060862


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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Robert Denk. Leonid Volevich. "Parameter-elliptic boundary value problems connected with the Newton polygon." Differential Integral Equations 15 (3) 289 - 326, 2002.


Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1008.35020
MathSciNet: MR1870644
Digital Object Identifier: 10.57262/die/1356060862

Primary: 35J40
Secondary: 46N20 , 47F05

Rights: Copyright © 2002 Khayyam Publishing, Inc.

Vol.15 • No. 3 • 2002
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