Homogenization of the Dirichlet problem for a system of quasilinear elliptic equations in a domain with fine-grained boundary

Mamadou Sango

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 2, page 183-212
  • ISSN: 0294-1449

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Sango, Mamadou. "Homogenization of the Dirichlet problem for a system of quasilinear elliptic equations in a domain with fine-grained boundary." Annales de l'I.H.P. Analyse non linéaire 20.2 (2003): 183-212. <http://eudml.org/doc/78576>.

@article{Sango2003,
author = {Sango, Mamadou},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {limit problem; capacitary methods},
language = {eng},
number = {2},
pages = {183-212},
publisher = {Elsevier},
title = {Homogenization of the Dirichlet problem for a system of quasilinear elliptic equations in a domain with fine-grained boundary},
url = {http://eudml.org/doc/78576},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Sango, Mamadou
TI - Homogenization of the Dirichlet problem for a system of quasilinear elliptic equations in a domain with fine-grained boundary
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 2
SP - 183
EP - 212
LA - eng
KW - limit problem; capacitary methods
UR - http://eudml.org/doc/78576
ER -

References

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  4. [4] Dal Maso G., An Introduction to Γ-convergence, Birkhauser, Boston, 1993. Zbl0816.49001
  5. [5] Dal Maso G., Garroni A., New results on the asymptotic behavior of Dirichlet problems in perforated domains, Math. Mod. Meth. Appl. Sci.3 (1994) 373-407. Zbl0804.47050MR1282241
  6. [6] Dal Maso G., Murat F., Dirichlet problems in perforated domains for homogeneous operators on H01, in: Calculus of Variations, Homogenization and Continuum Mechanics, World Scientific, Singapore, 1994, pp. 177-202. Zbl0884.47026
  7. [7] Dal Maso G., Murat F., Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators, Ann. Scuola Norm. Sup. Pisa, Cl. Sci.4 (1997) 24, No. 2, 239–290. Zbl0899.35007MR1487956
  8. [8] Ladyzhenskaya O.A., Uraltseva N.N., Linear and Quasilinear Elliptic Equations, Academic Press, New-York, 1968. Zbl0164.13002MR244627
  9. [9] Leray J., Lions J.L., Quelques resultats de Viŝik sur les problèmes élliptiques nonlinéaires par la méthode de Minty–Browder, Bull. Soc. Math. France93 (1965) 97-107. Zbl0132.10502MR194733
  10. [10] Marchenko V.A., Khruslov E.Ya., Boundary Value Problems in Domains With Fine-Grained Boundaries, Naukova Dumka, Kiev, 1974, (Russian). Zbl0289.35002
  11. [11] Moser J., A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math.13 (1960) 457-468. Zbl0111.09301MR170091
  12. [12] Oleinik O.A., Shamaev A.S., Yocifian G.A., Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam, 1992. Zbl0768.73003MR1195131
  13. [13] M. Sango, Pointwise a priori estimates for solutions of a system of quasilinear elliptic equations, Applicable Analysis, to appear. Zbl1034.35028MR1914687
  14. [14] Sango M., Homogenization of the Dirichlet problem for a system of quasilinear elliptic equations in a perforated domain, C. R. Acad. Sci. Paris329 (1999) 293-298. Zbl0933.35077MR1713334
  15. [15] Serrin J., Local behavior of solutions of quasi-linear equations, Acta Math.111 (1964) 247-302. Zbl0128.09101MR170096
  16. [16] Skrypnik I.V., Quasilinear Dirichlet problem for domains with fine-grained boundary, Dokl. Akad. Nauk Ukrain. SSR Ser. A2 (1982) 21-25. Zbl0485.35046MR650882
  17. [17] Skrypnik I.V., Methods for Analysis of Nonlinear Elliptic Boundary Value Problems, Nauka, Moscow, 1990, English translation in: Translations of Mathematical Monographs, Vol. 139, AMS, Providence, 1994. Zbl0822.35001MR1297765
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