Proprietà di approssimazione ℒ 2 di Runge e problema biarmonico generalizzato

Pieranita Castellani Rizzonelli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1979)

  • Volume: 66, Issue: 2, page 110-116
  • ISSN: 0392-7881

Abstract

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It is shown that, under very general hypotheses, the linear elliptic differential system Lu = 0 possesses the ℒ 2 Runge property when and only when the Dirichlet problem for the operator L ⁢ L * (i.e. the generalized biharmonic problem) has only one solution with a finite energy integral.

How to cite

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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 66.2 (1979): 110-116. <http://eudml.org/doc/288777>.

@article{CastellaniRizzonelli1979,
author = {Castellani Rizzonelli, Pieranita},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {ita},
month = {2},
number = {2},
pages = {110-116},
publisher = {Accademia Nazionale dei Lincei},
title = {Proprietà di approssimazione $\mathcal\{L\}^\{2\}$ di Runge e problema biarmonico generalizzato},
url = {http://eudml.org/doc/288777},
volume = {66},
year = {1979},
}

TY - JOUR
AU - Castellani Rizzonelli, Pieranita
TI - Proprietà di approssimazione $\mathcal{L}^{2}$ di Runge e problema biarmonico generalizzato
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1979/2//
PB - Accademia Nazionale dei Lincei
VL - 66
IS - 2
SP - 110
EP - 116
LA - ita
UR - http://eudml.org/doc/288777
ER -

References

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  1. Fichera, G. (1965) - Linear elliptic differential systems and eigenvalue problems, «Lecture Notes in Mathematics», N. 8, Springer Verlag, 1-176. Zbl0138.36104
  2. Lax, F.D. (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. Zbl0072.33004
  3. Malgrange, B. (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. Zbl0071.09002
  4. Browder, F.E. (1962) - Approximation by Solutions of Partial Differential Equations, «American Journal of Mathematics», Vol. 84, 134-160. Zbl0111.09601
  5. Fichera, G. (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. Walsh, J.L. (1935) - Interpolation and Approximation by Rational Functions in the Complex Domain, «American Math. Soc. Colloquium Publications», Vol. XX, 1-382. 

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