No loss of derivatives for hyperbolic operators with Zygmund-continuous coefficients in time

2020/01/24 by Colombini, Ferruccio, Del Santo, Daniele, Fanelli, Francesco
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.09202

Abstract

In this note we prove a well-posedness result, without loss of derivatives, for strictly hyperbolic wave operators having coefficients which are Zygmund-continuous in the time variable and Lipschitz-continuous in the space variables. The proof is based on Tarama's idea of introducing a lower order corrector in the energy, in order to produce special algebraic cancellations when computing its time derivative, combined with paradifferential calculus with parameters, in order to handle the low regularity of the coefficients with respect to x.

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