Abstract
An existence theorem is proved for the continuation form of the Cauchy problem Pu = ƒ(z, u(z), ▽u(z)), where P is a second order strictly hyperbolic differential operator, with initial data strongly conormal to three characteristic hypersurfaces intersecting at 0 and the light cone for P over 0. We assume that the hypersurfaces are either pairwisely transversal or two of them are tangent of finite order along the line of intersection. By reduction to a model case, conormal energy estimates are obtained for the linear equation with zero initial data. The proof of the theorem follows from an extension lemma and a contraction mapping argument.
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