Castellani Rizzonelli, Pieranita:
Proprietà di approssimazione $\mathcal{L}^{2}$ di Runge e problema biarmonico generalizzato
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 66 (1979), fasc. n.2, p. 110-116, (Italian)
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Sunto
It is shown that, under very general hypotheses, the linear elliptic differential system Lu = 0 possesses the $\mathcal{L}^{2}$ Runge property when and only when the Dirichlet problem for the operator $LL^{*}$ (i.e. the generalized biharmonic problem) has only one solution with a finite energy integral.
Referenze Bibliografiche
[1]
G. Fichera (
1965) -
Linear elliptic differential systems and eigenvalue problems, «
Lecture Notes in Mathematics», N.
8,
Springer Verlag, 1-176. |
Zbl 0138.36104[2]
F.D. Lax (
1956) -
A Stability Theorem for Solutions of Abstract Differential Equations and Its Application to the Study of the Local Behavior of Solutions of Elliptic Equations, «
Communications on Pure and Applied Mathematics», Vol.
IX, 747-766. |
Zbl 0072.33004[3]
B. Malgrange (
1955-1956) -
Existence et Approximation des Solutions des Équations aux Dérivées Partielles et des Équations de Convolution, «
Annales de l'Institut Fourier», Vol.
VI, 271-354. |
fulltext EuDML |
Zbl 0071.09002[4]
F.E. Browder (
1962) -
Approximation by Solutions of Partial Differential Equations, «
American Journal of Mathematics», Vol.
84, 134-160. |
Zbl 0111.09601[5] G. Fichera (1967) - Generalized Biharmonic Problem and Related Eingevalue Problems, Blanch Anniversary Volume, Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, 35-44.
[6] J.L. Walsh (1935) - Interpolation and Approximation by Rational Functions in the Complex Domain, «American Math. Soc. Colloquium Publications», Vol. XX, 1-382.
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