Characterization of algebraic curves that satisfy the Phragmén-Lindelöf principle for global evolution
type: Item
instance of: scholarly article
title: Characterization of algebraic curves that satisfy the Phragmén-Lindelöf principle for global evolution
zbMATH Open document ID: 1059.32009
DOI: 10.1007/BF03323377
author: Chiara Boiti
author: Reinhold Meise
published in: Results in Mathematics
publication date: 2004-11-26T00:00:00Z
review text: In some previous papers, \textit{C. Boiti} and \textit{M. Nacinovich} [Ann. Inst. Fourier 47, No. 1, 155--199 (1997; Zbl 0865.35091), Ann. Mat. Pura Appl., IV. Ser. 180, No. 1, 81--126 (2001; Zbl 1030.35128)] investigated the Cauchy problem, with initial data on an affine subvariety, for general (overdetermined) systems of partial differential operators with constant coefficients. In particular they characterized evolution in spaces of ultradifferentiable functions in terms of the validity of a Phragmén-Lindelöf maximum principle for plurisubharmonic functions on some associated complex algebraic variety. In this paper, using also the results obtained by \textit{R. Meise, B. A. Taylor} and \textit{D. Vogt} [J. Am. Math. Soc. 11, No. 1, 1--39 (1998; Zbl 0896.32008)] and by \textit{R. W. Braun, R. Meise} and \textit{B. A. Taylor} [Trans. Am. Math. Soc. 356, No. 4, 1315--1383 (2004; Zbl 1039.32010)], quite explicit conditions for evolution in spaces of ultradifferentiable functions are found for the case where the associated complex algebraic variety is a plane curve \(V\). First it is shown that in the homogeneous case all points at infinity must be real; next necessary and sufficient conditions for the general curve are found in terms of its branching at infinity, described in terms of Puiseux series expansions. In the last section these results are illustrated by examples and also to study evolution for some overdetermined systems (the curve \(V\) is no longer assumed to be planar).
reviewed by: Mauro Nacinovich
Mathematics Subject Classification ID: 32U05
Mathematics Subject Classification ID: 35E99
Mathematics Subject Classification ID: 35L99
zbMATH DE Number: 2119241
zbMATH Keywords: Phragmén-Lindelöf conditions
zbMATH Keywords: ultradifferentiable functions
zbMATH Keywords: evolution equations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2119241