$C^{1,\alpha}$ regularity of the blow-up curve at non characteristic points for the one dimensional semilinear wave equation.
Résumé
We consider $u(x, t)$ a blow-up solution of $\partial_{tt}u = \partial{xx}u + |u|p−1u$, that blows-up in one space dimension. We consider its blow-up curve $T (x)$ and $R$ the set of non characteristic points. We prove that $T (x)$ is of class $C^{1,\alpha}$ in $R$.
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