## Propagation of $$C^{\infty}$$ regularity for fully nonlinear second order strictly hyperbolic equations in two variables.(English)Zbl 0549.35087

It is shown that if u is a $$C^ 3$$ solution of a fully nonlinear second order strictly hyperbolic equation in two variables, then u is $$C^{\infty}$$ at a point m as soon as it is $$C^{\infty}$$ at some point of each of the two bicharacteristic curves through m. For semilinear equations, such a result was obtained before by Rauch and Reed if $$u\in C^ 1$$.

### MSC:

 35L70 Second-order nonlinear hyperbolic equations 35A30 Geometric theory, characteristics, transformations in context of PDEs
Full Text: