In this paper we study the convergence properties of Newton's sequence for analytic systems of equations with constant rank derivatives. Our main result is an alpha-theorem which ensures the convergence of Newton's sequence to a leastsquare solution of this system.
Hypoelliptic systems connected with Newton's polyhedron
✍ Scribed by Chikh Bouzar; Leonid Volevich
- Publisher
- John Wiley and Sons
- Year
- 2004
- Tongue
- English
- Weight
- 188 KB
- Volume
- 273
- Category
- Article
- ISSN
- 0025-584X
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✦ Synopsis
Abstract
We introduce a general class of hypoelliptic systems of partial differential operators with variable coefficients generalizing the so‐called multi‐quasi‐elliptic differential operators. We study the regularity of solutions of these systems. More complete results are obtained in the case of two independent variables. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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