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On the continuity of the solution operator to the wave map system
Author(s) -
D'Ancona Piero,
Georgiev Vladimir
Publication year - 2004
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3043
Subject(s) - counterexample , mathematics , operator (biology) , dimension (graph theory) , class (philosophy) , hölder condition , mathematical analysis , pure mathematics , discrete mathematics , computer science , artificial intelligence , biochemistry , chemistry , repressor , transcription factor , gene
We investigate the continuity properties of the solution operator to the wave map system from ℝ × ℝ n to a general nonflat target of arbitrary dimension, and we prove by an explicit class of counterexamples that this map is not uniformly continuous in the critical norms on any neighborhood of 0. © 2003 Wiley Periodicals, Inc.