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Zbl 0804.35092
Ehrenpreis, Leon
Exotic parametrization problems. (English)
[J] Ann. Inst. Fourier 43, No.5, 1253-1266 (1993). ISSN 0373-0956; ISSN 1777-5310/e

We study the problem of parametrizing solutions of an overdetermined system of linear partial differential equations $\{P\sb j(X,D)f=0\}$. In the classical parametrization problems, such as the Cauchy and Dirichlet problems, the data are given on a manifold $M$ whose dimension $d$ is well-determined by the equations. In exotic problems the data are given on manifolds with dimension $\ne d$.\par If the data are given on a manifold $M$ of dimension $>d$ then the data must satisfy certain equations. If $M$ is a hyperspace then these equations are differential equations and there are finitely many of them. In case $\dim M<d$ infinitely many data are prescribed. Explicit examples are given for the wave equation on a time-like line and on a space-like line.\par An extension of the ``thin edge-of-the-wedge'' theorem to partial differential equations is given.
[L.Ehrenpreis (Philadelphia)]

MSC 2000:: *35N10 Overdetermined systems of PDE with variable coefficients, general

Keywords: parametrization problems

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