In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coecients in any space dimension N ≥ 1. We will suppose the coecients to be log-Zygmund continuous in time and log-Lipschitz continuous in space. Paradierential calculus with parameters will be the main tool to get energy estimates in Sobolev spaces and these estimates will present a time-dependent loss of derivatives.

No abstract

No abstract

No abstract

We investigate the relation between the backward uniqueness and the regularity of the coefficients for a parabolic operator. A necessary and sufficient condition for uniqueness is given in terms of the modulus of continuity of the coefficients