On homogeneizatìon problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities.
Oleinik, Olga A. ; Shaposhnikova, Tatiana
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 6 (1995), p. 133-142 / Harvested from Biblioteca Digitale Italiana di Matematica
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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.

In questa Nota viene studiato il problema della omogeneizzazione per l'operatore di Laplace in domini parzialmente perforati con piccole cavità e con condizioni di Neumann nel contorno delle cavità. Viene anche considerato il corrispondente problema spettrale.

Publié le : 1995-10-01
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     author = {Olga A. Oleinik and Tatiana Shaposhnikova},
     title = {On homogeneizat\`\i on	problems for the Laplace operator in partially perforated domains with Neumann's condition on the boundary of cavities.},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {6},
     year = {1995},
     pages = {133-142},
     zbl = {0848.35009},
     mrnumber = {1363782},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1995_9_6_3_133_0}
}

Oleinik, Olga A.; 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, Tome 6 (1995) pp. 133-142. http://gdmltest.u-ga.fr/item/RLIN_1995_9_6_3_133_0/

[1] Marchenko, V. A. - Khruslov, E. Ya., Boundary Value Problems in Domains with a Fine Grained Boundary. Naukova Dumka, Kiev 1974. | MR 601059 | Zbl 0289.35002

[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. | Zbl 0496.35030

[3] Cioranescu, D. - Saint Jean Paulin, J., Homogeneization in open sets with holes. J. Math. Anal. Appl., 71, 1979, 590-607. | MR 548785 | Zbl 0427.35073

[4] Oleinik, O. A. - Yosifian, G. A. - Shamaev, A. S., Mathematical Problems in Elasticity and Homogeneization. North-Holland, Amsterdam 1992. | MR 1195131 | Zbl 0768.73003

[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. | MR 1260777 | Zbl 0923.35022

[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, Heidelberg 1993.

[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. | MR 1348290 | Zbl 0854.35010

[9] Oleinik, O. A. - Shaposhnikova, T. A., On homogeneization problems in partially perforated domains. Russian Math. Survey, vol. 50, n. 4, 1995.