Perron’s method for second order hyperbolic PDE. Part III

We continue Part I of this paper. Here, in Part III, comparison principles are proved for nonsmooth sub and super solutions (with nonsmooth Cauchy data) of semilinear hyperbolic PDE in compact regular domains of R+ × R+ when n 3, and existence of a nonsmooth solution to the nonsmooth Cauchy problem is proved by a Perron-like method.  2003 Elsevier Inc. All rights reserved