On the continuity of the solution operator to the wave map system

Piero D'Ancona; Vladimir Georgiev

doi:10.1002/cpa.3043

On the continuity of the solution operator to the wave map system

Piero D'Ancona^*, Vladimir Georgiev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

We investigate the continuity properties of the solution operator to the wave map system from ℝ × ℝⁿ 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.

Original language	English
Pages (from-to)	357-383
Number of pages	27
Journal	Communications on Pure and Applied Mathematics
Volume	57
Issue number	3
DOIs	https://doi.org/10.1002/cpa.3043
Publication status	Published - 2004 Mar
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1002/cpa.3043

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abstract = "We investigate the continuity properties of the solution operator to the wave map system from ℝ × ℝn 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.",

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AU - Georgiev, Vladimir

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AB - We investigate the continuity properties of the solution operator to the wave map system from ℝ × ℝn 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.

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On the continuity of the solution operator to the wave map system

Abstract

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