PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1993 | 107 | 2 | 157-169
Tytuł artykułu

A partial differential operator which is surjective on Gevrey classes $Γ^{d}(ℝ³)$ with 1 ≤ d < 2 and d ≥ 6 but not for 2 ≤ d < 6

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is shown that the partial differential operator $P(D) = ∂⁴/∂x⁴ - ∂²/∂y² + i∂/∂z : Γ^d(ℝ³) → Γ^d(ℝ³)$ is surjective if 1 ≤ d < 2 or d ≥ 6 and not surjective for 2 ≤ d < 6.
Słowa kluczowe
Czasopismo
Rocznik
Tom
107
Numer
2
Strony
157-169
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-11-30
poprawiono
1993-04-27
Twórcy
Bibliografia
  • [1] L. V. Ahlfors, Conformal Invariants, McGraw-Hill, New York, 1973.
  • [2] R. W. Braun, R. Meise and B. A. Taylor, Ultradifferentiable functions and Fourier analysis, Resultate Math. 17 (1990), 206-237.
  • [3] R. W. Braun, R. Meise and D. Vogt, Applications of the projective limit functor to convolution and partial differential equations, in: Advances in the Theory of Fréchet Spaces, Proc. Istanbul 1987, T. Terzioğlu (ed.), NATO Adv. Sci. Inst. Ser. C 287, Kluwer, 1989, 29-46.
  • [4] R. W. Braun, R. Meise and D. Vogt, Characterization of the linear partial differential operators with constant coefficients which are surjective on non-quasianalytic classes of Roumieu type on $ℝ^N$, preprint.
  • [5] L. Cattabriga, Solutions in Gevrey spaces of partial differential equations with constant coefficients, in: Analytic Solutions of Partial Differential Equations, Proc. Trento 1981, L. Cattabriga (ed.), Astérisque 89/90 (1981), 129-151.
  • [6] L. Cattabriga, On the surjectivity of differential polynomials on Gevrey spaces, in: Atti del Convegno: 'Linear Partial and Pseudodifferential Operators', Rend. Sem. Mat. Univ. Politec. Torino, fascicolo speziale, 1983, 81-89.
  • [7] E. De Giorgi e 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.
  • [8] L. Hörmander, On the existence of real-analytic solutions of partial differential equations with constant coefficients, Invent. Math. 21 (1973), 151-183.
  • [9] R. Meise, B. A. Taylor and D. Vogt, Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse, Ann. Inst. Fourier (Grenoble) 40 (1990), 619-655.
  • [10] L. C. Piccinini, Non surjectivity of the Cauchy-Riemann operator on the space of the analytic functions on $R^n$. Generalization to the parabolic operators, Boll. Un. Mat. Ital. (4) 7 (1973), 12-28.
  • [11] G. Zampieri, An application of the Fundamental Principle of Ehrenpreis to the existence of global Gevrey solutions of linear partial differential equations, ibid. (6) 5-B (1986), 361-392.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv107i2p157bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.