FUCHSIAN EQUATIONS IN SOBOLEV SPACES AND BLOW-UP

We construct solutions of square u = e(u) which blow-up precisely on a given space-like hypersurface of class H-s. For this purpose, we prov e a general existence theorem for Fuchsian PDE in Sobolev spaces. The precise relation between the regularity of the data and that of thr so lution is shown to involve logarithmic symbols, in a model situation. A few further results on power nonlinearities are also included. (C) 1 996 Academic Press, Inc.