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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
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