UNIQUENESS AND CONTINUOUS DEPENDENCE OF CAUCHY PROBLEM FOR LINEAR PARTIAL DIFFERENTIAL EQUATIONS

In this paper, we investigate the connection between the uniqueness and the continuousdependence of the Cauchy problem for general linear partial differential equations. First thelocal Carleman’s estimate used by Calderon to prove the uniqueness is extended to the globalestimate with a specifie peaking weight factor. Then using this estimate, we can derive notonly the uniqueness of solution but also the continuous dependence of the solution in the F.John sense.