Cattabriga, Lamberto and Zanghirati, Luisa:
Global analytic and Gevrey surjectivity of the Mizohata operator \( D_2 + i x^{2k}_{2} D_{1} \) (Suriettività globale, analitica e di Gevrey, dell'operatore di Mizohata \( D_2 + i x^{2k}_{2} D_{1} \))
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 1 (1990), fasc. n.1, p. 37-39, (English)
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Sunto
Si prova che l'operatore \( D_2 + i x^{2k}_{2} D_{1} \) è suriettivo dallo spazio di Gevrey \( \mathcal{E}^{\{s\}}(\mathbb{R}^{2}) \), \( s \geq 1 \), su sé stesso e che ciò non accade per lo stesso operatore da \( \mathcal{E}^{\{s\}}(\mathbb{R}^{3}) \) ad \( \mathcal{E}^{\{s\}}(\mathbb{R}^{3}) \).
Referenze Bibliografiche
[1]
R. W. BRAUN -
R. MEISE -
D. VOGT,
Applications of the projective limit functor to convolution and partial differential equations.
Proceeding of the NATO ASW on Fréchet spaces, Istanbul, August 1988,
D. Reidel Publishing Comp. (to appear). |
MR 1083556 |
Zbl 0726.46022[2]
L. CATTABRIGA,
Solutions in Gevrey spaces of partial differential equations with constant coefficients.
Astérisque,
89-90,
1981, 129-151. |
MR 666406 |
Zbl 0496.35018[3]
L. CATTABRIGA,
On the surjectivity of differential polynomials on Gevrey spaces.
Rend. Sem. Mat. Univ. Politec. Torino, Fasc. speciale, Convegno Linear partial and pseudodifferential operators, Torino, 30 Sett. - 2 Ott. 1982,
41,
1983, 81-89. |
MR 745976 |
Zbl 0561.35008[4]
E. DE GIORGI,
Solutions analytiques des équations aux dérivées partielles à coefficients constants.
Séminaire Goulauic-Schwartz 1971-72, Equations aux dérivées partielles et analyse fonctionelle, Exp. N. 29, Ecole Polytech. Centre de Math., Paris
1972. |
fulltext mini-dml |
fulltext mini-dml |
MR 397137 |
Zbl 0244.35017[5]
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. Un. Mat. Ital. (4),
4,
1971, 1015-1027. |
MR 382820 |
Zbl 0224.35018[7]
J. FRIBERG,
Estimates for partially hypoelliptic differential operators.
Medd. Lund Univ. Mat. Sem.,
17,
1963, 1-93. |
MR 157109 |
Zbl 0139.28403[8]
L. HÖRMANDER,
On the existence of real analytic solutions of partial equations with constant coefficients.
Inventiones Math.,
21,
1973, 151-182. |
MR 336041 |
Zbl 0282.35015[9]
L. HÖRMANDER,
The analysis of linear partial differential operators.
Springer Verlag, vol.
IV,
1983. |
Zbl 0521.35002[11] T. KAWAI, On the global existence of real analytic solutions and hyperfunction solutions of linear differential equations. Publ. RIMS Kyoto University, 555, 1986.
[12]
H. KOMATSU,
An analogue of the Cauchy-Kowalevsky theorem for ultradifferentiable functions and a division theorem of ultradistributions as its dual.
J. Fac. Sci. Univ. Tokyo, Sec. IA,
26,
1979, 239-254. |
MR 550685 |
Zbl 0424.46032[14]
L. RODINO,
On linear partial differential operators with multiple characteristics.
Proceedings Conf. on Partial Differential Equations (Holzhau, GDR, 1988),
Teubner Text zur Mathematik. |
MR 1105815 |
Zbl 0681.35093[15]
G. ZAMPIERI,
An application of the fundamental principle of Ehrenpreis to the existence of global Gevrey solutions of linear differential equations.
Boll. Un. Mat. It. (6),
V-B,
1986, 361-392. |
MR 860634 |
Zbl 0624.35011
Con il contributo del Ministero per i Beni e le Attività Culturali