On homogeneizatìon problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities.

Olga A. Oleinik; Tatiana Shaposhnikova

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1995)

  • Volume: 6, Issue: 3, page 133-142
  • ISSN: 1120-6330

Abstract

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In this paper the problem of homogeneization for the Laplace operator in partially perforated domains with small cavities and the Neumann boundary conditions on the boundary of cavities is studied. The corresponding spectral problem is also considered.

How to cite

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Oleinik, Olga A., and Shaposhnikova, Tatiana. "On homogeneizatìon problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities.." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 6.3 (1995): 133-142. <http://eudml.org/doc/244085>.

@article{Oleinik1995,
abstract = {In this paper the problem of homogeneization for the Laplace operator in partially perforated domains with small cavities and the Neumann boundary conditions on the boundary of cavities is studied. The corresponding spectral problem is also considered.},
author = {Oleinik, Olga A., Shaposhnikova, Tatiana},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Homogeneization; Perforated domains; Small cavities; Neumann's condition; Spectral problem; perforated domains; small cavities; Neumann boundary condition},
language = {eng},
month = {10},
number = {3},
pages = {133-142},
publisher = {Accademia Nazionale dei Lincei},
title = {On homogeneizatìon problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities.},
url = {http://eudml.org/doc/244085},
volume = {6},
year = {1995},
}

TY - JOUR
AU - Oleinik, Olga A.
AU - Shaposhnikova, Tatiana
TI - On homogeneizatìon problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities.
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1995/10//
PB - Accademia Nazionale dei Lincei
VL - 6
IS - 3
SP - 133
EP - 142
AB - In this paper the problem of homogeneization for the Laplace operator in partially perforated domains with small cavities and the Neumann boundary conditions on the boundary of cavities is studied. The corresponding spectral problem is also considered.
LA - eng
KW - Homogeneization; Perforated domains; Small cavities; Neumann's condition; Spectral problem; perforated domains; small cavities; Neumann boundary condition
UR - http://eudml.org/doc/244085
ER -

References

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  1. MARCHENKO, V. A. - KHRUSLOV, E. YA., Boundary Value Problems in Domains with a Fine Grained Boundary. Naukova Dumka, Kiev1974. Zbl0289.35002MR601059
  2. CIORANESCU, D. - MURAT, F., Un terme étranger venu d'ailleurs, 1 & 2. In: H. BREZIS, J.-L. LIONS (eds.), Nonlinear partial differential equations and their application. College de France Seminar, vol. 2-3. Research in Math., 60-70, Pitman, 1982, 98-138, 154-178. Zbl0496.35030
  3. CIORANESCU, D. - SAINT JEAN PAULIN, J., Homogeneization in open sets with holes. J. Math. Anal. Appl., 71, 1979, 590-607. Zbl0427.35073MR548785DOI10.1016/0022-247X(79)90211-7
  4. OLEINIK, O. A. - YOSIFIAN, G. A. - SHAMAEV, A. S., Mathematical Problems in Elasticity and Homogeneization. North-Holland, Amsterdam1992. Zbl0768.73003MR1195131
  5. BELIAEV, A. G., Asymptotic of solutions of the Dirichlet problem for the Poisson equation in a perforated domain with small cavities. Russian Math. Survey, vol. 44, n. 4, 1989, 231. 
  6. JÄGER, W. - OLEINIK, O. A. - SHAMAEV, A. S., On homogeneization problem for the Laplace operator in partially perforated domain. Doklady RAS, vol. 333, n. 4, 1993, 424-427. Zbl0923.35022MR1260777
  7. JÄGER, W. - OLEINDC, O. A. - SHAMAEV, A. S., On a homogeneization problem for the Laplace operator in a partially perforated domain with the Neumann condition on holes. Preprint 93-53, Inter-Disziplinäres Zentrum für Wissenschaftliches Rechnen, Heidelberg1993. 
  8. OLEINIK, O. A. - SHAPOSHNIKOVA, T. A., On an approach of constructing of approximations in homogeneization problems for partially perforated domain. Diff. Equations, vol. 30, n. 11, 1994, 1994-1999. Zbl0854.35010MR1348290
  9. OLEINIK, O. A. - SHAPOSHNIKOVA, T. A., On homogeneization problems in partially perforated domains. Russian Math. Survey, vol. 50, n. 4, 1995. 

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