University of Ferrara, via Machiavelli 35, 44100 Ferrara, Italy ; University of Bologna, via Genova 181, 47023 Cesena, Italy
Abstract:
We prove the well-posedness of the forward Cauchy problem for a pseudo-differential operator of order with the Log-Lipschitz continuous symbol in the time variable. The characteristic roots of are distinct and satisfy the necessary Lax-Mizohata condition Im . The Log-Lipschitz regularity has been tested as the optimal one for well-posedness in the case of second-order hyperbolic operators. Our main aim is to present a simple proof which needs only a little of the basic calculus of standard pseudo-differential operators.