Wave equations with low regularity coefficients (Q1126752)

This paper is a review of recent developments on the understanding of solutions of wave equations on Riemannian manifolds with metrics of low differentiability. The objective is to prove a type of Strichartz estimate which is deduced by an interpolation argument. At one of the end points the above mentioned estimate is not valid. Also the author states two results: The first one proves that a minimal regularity of the metric is necessary, and the other which proves that the inequality is true if hypothesis on the sectional curvature is made.