The Cauchy Problem for Wave Equations with NonLipschitz Coefficients

Details The Cauchy Problem for Wave Equations with NonLipschitz Coefficients The Cauchy Problem for Wave Equations with NonLipschitz Coefficients

2006-11-14

arxiv.org/abs/math/0611426v1

Mathematics

Analysis of PDEs

44 pages

Scientific paper

In this paper we study the Cauchy problem for second order strictly hyperbolic operators when the coefficients of the principal part are not Lipschitz continuous, but only "Log-Lipschitz" with respect to all the variables. This class of equation is invariant under changes of variables and therefore suitable for a local analysis. In particular, we show local existence, local uniqueness and finite speed of propagation for the noncharacteristic Cauchy problem.

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