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.
On the continuity of the solution operator to the wave map system / D'Ancona, Piero Antonio; Gueorguiev, Vladimir. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - STAMPA. - 57:(2004), pp. 357-383. [10.1002/cpa.3043]
On the continuity of the solution operator to the wave map system
D'ANCONA, Piero Antonio;GUEORGUIEV, VLADIMIR
2004
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.File allegati a questo prodotto
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