Non-Markovian quadratic forms obtained by homogenization
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 323-337.

Voir la notice de l'article dans Biblioteca Digitale Italiana di Matematica

Questo articolo riguarda il comportamento asintotico delle forme quadratiche definite in $L^{2}$. Più precisamente consideriamo la $\Gamma$-convergenza di questi funzionali per la topologia debole di $L^{2}$. Noi diamo un esempio in cui certe forme limite non sono Markoviane e quindi la formula di Beurling-Deny non si applica. Questo esempio è ottenuto tramite l'omogeneizzazione di un materiale stratificato composto da strati sottili isolanti.
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Briane, Marc. Non-Markovian quadratic forms obtained by homogenization. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 323-337. https://geodesic-test.mathdoc.fr/item/BUMI_2003_8_6B_2_a3/

[1] T. Arbogast-J. Douglas-U. Hornung, Derivation of the double porosity model of single phase flow via homogenization theory, S.I.A.M. J. Math. Anal., 21 (1990), 823-836. | MR | Zbl

[2] M. Bellieud-G. Bouchitté, Homogenization of elliptic problems in a fiber reinforced structure. Nonlocal effects, Annali della Scuola Normale Superiore di Pisa, 26, (4) (1998), 407-436. | fulltext mini-dml | MR | Zbl

[3] M. Bellieud-G. Bouchitté, Homogenization of degenerate elliptic equations in a fiber structure, preprint 98/09 ANLA, Univ. Toulon.

[4] A. Beurling-J. Deny, Espaces de Dirichlet, Acta Matematica, 99 (1958), 203-224. | MR | Zbl

[5] A. Beurling-J. Deny, Dirichlet spaces, Proc. Nat. Acad. Sci. U.S.A., 45 (1959), 208-215. | MR | Zbl

[6] M. Briane, Homogenization in some weakly connected domains, Ricerche di Matematica, XLVII, no. 1 (1998), 51-94. | MR | Zbl

[7] G. Dal Maso, An introduction to $\Gamma$-convergence, Birkhäuser, Boston (1993). | MR | Zbl

[8] V. N. Fenchenko-E. Ya. Khruslov, Asymptotic of solution of differential equations with strongly oscillating and degenerating matrix of coefficients, Dokl. AN Ukr. SSR, 4 (1980). | Zbl

[9] M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland Math. Library, 23, North-Holland and Kodansha, Amsterdam (1980). | MR | Zbl

[10] E. Ya. Khruslov, The asymptotic behavior of solutions of the second boundary value problems under fragmentation of the boundary of the domain, Maths. USSR Sbornik, 35, no. 2 (1979). | Zbl

[11] E. Ya. Khruslov, Homogenized models of composite media, Composite Media and Homogenization Theory, G. Dal Maso and G. F. Dell'Antonio editors, in Progress in Nonlinear Differential Equations and Their Applications, Birkhäuser (1991), 159-182. | MR | Zbl

[12] Y. Le Jean, Mesures associées à une forme de Dirichlet. Applications, Bull. Soc. Math. de France, 106 (1978), 61-112. | fulltext mini-dml | Zbl

[13] U. Mosco, Composite media and asymptotic Dirichlet forms, Journal of Functional Analysis, 123, no. 2 (1994), 368-421. | MR | Zbl