The cauchy problem at simply characteristic points andP-convexity |
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Authors: | Jan Persson |
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Institution: | 1. Troms?, Norvegia
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Abstract: | Summary Let Ω cR
n be an open set and let P be a linear partial differential operator with constant coefficients inR
n. Then Ω is said to be P-convex if for each f ε C∞(Ω) there is a u ε D′(Ω) such that P(D)u=f. A complete geometric characterization of P-convex sets inR
3 is given when P is of principal type and when Ω has C2-boundary. As a step in the proof one also obtains necessary and sufficient conditions for uniqueness in the local Cauchy
problem at simply characteristic points inR
3. The tools are a sophisticated use of the author's uniqueness cones on one hand and his semi-global nullsolutions on the
other hand. Hints are given on the difficulties that may be encountered inR
n for the same problem.
Entrata in Redazione il 7 giugno 1978. |
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Keywords: | |
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