Propagation of $C^ \infty$ regularity for fully nonlinear second order strictly hyperbolic equations in two variables
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- by Paul Godin PDF
- Trans. Amer. Math. Soc. 290 (1985), 825-830 Request permission
Abstract:
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 $u \in {C^1}$References
- Hans Lewy, Über das Anfangswertproblem einer hyperbolischen nichtlinearen partiellen Differentialgleichung zweiter Ordnung mit zwei unabhängigen Veränderlichen, Math. Ann. 98 (1928), no. 1, 179–191 (German). MR 1512399, DOI 10.1007/BF01451588
- Jeffrey Rauch and Michael C. Reed, Propagation of singularities for semilinear hyperbolic equations in one space variable, Ann. of Math. (2) 111 (1980), no. 3, 531–552. MR 577136, DOI 10.2307/1971108
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 290 (1985), 825-830
- MSC: Primary 35L70; Secondary 35L67
- DOI: https://doi.org/10.1090/S0002-9947-1985-0792830-8
- MathSciNet review: 792830