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Zampieri, Giuseppe

A link between \(C^\infty\) and analytic solvability for P.D.E. with constant coefficients. (English) Zbl 0471.35017

Rend. Sem. Mat. Univ. Padova 63, 145-150 (1980).
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MSC:

35E20 General theory of PDEs and systems of PDEs with constant coefficients
35E10 Convexity properties of solutions to PDEs with constant coefficients
35A20 Analyticity in context of PDEs
35E05 Fundamental solutions to PDEs and systems of PDEs with constant coefficients
32T99 Pseudoconvex domains

Keywords:

linear partial differential operator with constant coefficients; analytic solution; P-convex
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\textit{G. Zampieri}, Rend. Semin. Mat. Univ. Padova 63, 145--150 (1980; Zbl 0471.35017)
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References:

[1] E. De GIORGI - L. CATTABRIGA, Una dimostrazione diretta dell’esistenza di soluzioni analitiche nel piano reale di equazioni a derivate parziali a coefficienti costanti , Boll. U.M.I. , 4 ( 1971 ), pp. 1015 - 1027 . MR 382820 | Zbl 0224.35018 · Zbl 0224.35018
[2] A. Grothendieck , Espaces vectoriels topologiques, publicação da Societade de Matematica de San Paulo , 2^\circ ediçao, 1958 . MR 77884 | Zbl 0316.46001 · Zbl 0316.46001
[3] L. Hörmander , Linear partial differential operators , Springer-Verlag , 1963 . MR 404822 | Zbl 0108.09301 · Zbl 0108.09301
[4] L. Hörmander , On the existence of real analytic solutions of partial differential equations with constant coefficients , Inventiones math. , 21 ( 1973 ), pp. 151 - 182 . MR 336041 | Zbl 0282.35015 · Zbl 0282.35015
[5] F. Mantovani - S. Spagnolo , Funzionali analitici reali e funzioni armoniche , Ann. Sc. Norm. Sup. Pisa , Cl. Sci. Mat. Fis. Natur., III Sez. , 18 ( 1964 ), pp. 475 - 513 . Numdam | MR 174965 | Zbl 0134.11102 · Zbl 0134.11102
[6] G. Zampieri , A sufficient condition for existence of real analytic solutions of P.D.E. with constant coefficients, in open sets of R2 , Rend. Sem. Mat. Univ. Padova , 63 ( 1980 ). Numdam | Zbl 0499.35021 · Zbl 0499.35021
[7] G. Zampieri , Un’estensione del teorema sulle suriezioni fra spazi di Fréchet. Qualche sua applicazione , Rend. Sem. Mat. Univ. Padova , 61 ( 1979 ). Numdam | MR 569657 | Zbl 0456.35010 · Zbl 0456.35010
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