On the prolongation of solutions for quasilinear differential equations (Q1057420)

It is known that holomorphic solutions of linear partial differential equations can be holomorphically continued across non-characteristic surfaces. This is also true for quasilinear equations of order m if the derivatives of the solutions up to order \(m+1\) are bounded [see \textit{Y. Tsuno}, J. Math. Soc. Japan 27, 454-466 (1975; Zbl 0303.35011)]. On the other hand, there are solutions of semilinear equations which are singular along non-characteristic surfaces. In the present paper the author announces an improvement of Tsuno's result: for each quasilinear equation of order m there is an exponent \(s\leq m-1\) such that boundedness of the derivatives of order up to (and including) s is already sufficient for prolongation.