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Uniqueness for critical nonlinear wave equations and wave maps via the energy inequality

✍ Scribed by Michael Struwe

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
60 KB
Volume
52
Category
Article
ISSN
0010-3640

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✦ Synopsis

We show uniqueness of sufficiently regular solutions to critical semilinear wave equations and wave maps in the (a priori) much larger class of distribution solutions with finite energy, assuming only that the energy is nonincreasing in time.

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## Abstract We prove unique continuation of solutions of the wave equation along and across lower‐dimensional planes containing the __t__‐axis. This is a sharpening and a generalization of a result of Cheng, Ding and Yamamoto as well as a simplification of the proof. Copyright Β© 2008 John Wiley & S