## A parametrix construction for wave equations with $$C^{1,1}$$ coefficients.(English)Zbl 0974.35068

Summary: We give a construction of the wave group for variable coefficient, time dependent wave equations, under the hypothesis that the coefficients of the principal term possess two bounded derivatives in the spatial variables, and one bounded derivative in the time variable. We use this construction to establish the Strichartz and Pecher estimates for solutions to the Cauchy problem for such equations, in space dimensions $$n=2$$ and $$n=3$$.

### MSC:

 35L05 Wave equation 35R05 PDEs with low regular coefficients and/or low regular data 35L15 Initial value problems for second-order hyperbolic equations 35S30 Fourier integral operators applied to PDEs 35S50 Paradifferential operators as generalizations of partial differential operators in context of PDEs
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