Nonexistence of isolated singularities for nonlinear systems of partial differential equations and some applications (Q1127107)

This paper deals with the nonexistence of isolated singularities of the classical solutions of several classes of nonlinear systems and equations appearing in gas dynamics (Tricomi, Tay Ping Liu and Xin, Oleinik, B. Kheifitz) and in differential geometry (Monge-Ampère). The techiques of nonlinear microlocal analysis and more specially, the paradifferential approach, enables the author to prove a theorem for the nonexistence of isolated singularities in the microlocal Sobolev spaces. The main assumptions are imposed on the linearization (first variation) of the system under consideration. An application to the two-dimensional Monge-Ampère equation with a Gaussian curvature changing its sign is given.