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• W2034606979 abstract "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." @default.
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• W2034606979 date "1979-12-01" @default.
• W2034606979 modified "2023-10-05" @default.
• W2034606979 title "The cauchy problem at simply characteristic points andP-convexity" @default.
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• W2034606979 doi "https://doi.org/10.1007/bf02411691" @default.
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