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A theorem on homogeneous differential polynomials in $$R^ 2$$. (Italian) Zbl 0546.35010
The author shows that a theorem of G. Bratti [ibid. 69, 169-180 (1983)] on operators $$P(D_ x,D_ y)$$ with constant coefficients can be proved by a more geometric method if P is homogeneous. The main part of the paper is the proof of $$D_ x(G(B))=G(B)$$ for $$D_ x$$-convex sets $$B\subset {\mathbb{R}}^ 2$$, $$(G(B)=\{f\in C^{\infty}({\mathbb{R}}^ 2):f|_ B=0\}).$$
Reviewer: W.Watzlawek
MSC:
 35E10 Convexity properties of solutions to PDEs with constant coefficients 35G05 Linear higher-order PDEs
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References:
 [1] G. Bratti , Problema di Cauchy semiglobale in due variabili , in stampa presso Rend. Sem. Mat. di Padova. [2] L. Hormander , Linear partial differential operators , Springer-Verlag , 1969 . MR 404822 | Zbl 0175.39201 · Zbl 0175.39201
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