A discrete phenomenon in the C∞ and analytic regularity of the blow-up curve of solutions to the Liouville equation in one space dimension

We give a complete discussion of the C∞ or analytic regularity of blow-up curves for Cauchy problems or some mixed problems for the Liouville equation in one space dimension. In the case of mixed problems, the regularity results depend on the boundary condition: actually, we show the existence of a sequence of boundary conditions for which the regularity of the blow-up curve is better than in the general case. © 2002 Elsevier Science (USA).SCOPUS: ar.j