In this paper we obtain an energy estimate for a complete strictly hyperbolic operator with second order coefficients satisfying a log-Zygmund-continuity condition with respect to $t$, uniformly with respect to $x$, and a log-Lipschitz-continuity condition with respect to $x$, uniformly with respect to $t$.

1 aColombini, Ferruccio1 aFanelli, Francesco uhttps://www.math.sissa.it/publication/note-non-homogeneous-hyperbolic-operators-low-regularity-coefficients