Non-homogeneous Neumann problems in domains with small holes

C. Conca; P. Donato

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1988)

  • Volume: 22, Issue: 4, page 561-607
  • ISSN: 0764-583X

How to cite

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Conca, C., and Donato, P.. "Non-homogeneous Neumann problems in domains with small holes." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 22.4 (1988): 561-607. <http://eudml.org/doc/193542>.

@article{Conca1988,
author = {Conca, C., Donato, P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Poisson equation; perforated domain; periodically distributed holes; convergences; renormalized solution},
language = {eng},
number = {4},
pages = {561-607},
publisher = {Dunod},
title = {Non-homogeneous Neumann problems in domains with small holes},
url = {http://eudml.org/doc/193542},
volume = {22},
year = {1988},
}

TY - JOUR
AU - Conca, C.
AU - Donato, P.
TI - Non-homogeneous Neumann problems in domains with small holes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1988
PB - Dunod
VL - 22
IS - 4
SP - 561
EP - 607
LA - eng
KW - Poisson equation; perforated domain; periodically distributed holes; convergences; renormalized solution
UR - http://eudml.org/doc/193542
ER -

References

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  1. [1] H. ATTOUCH, Variational convergence for functions and operators, Pitman Applicable Mathematics Series, Pitman, London, 1984. Zbl0561.49012MR773850
  2. [2] A. BENSOUSSAN, J. L. LIONS, G. PAPANICOLAOU, Asymptotic analysis for periodic structures, North-Holland, Amsterdam, 1978. Zbl0404.35001MR503330
  3. [3] D. CIORANESCU, P. DONATO, Homogénéisation du problème de Neumann non-homogène dans des ouverts perforés, Asymptotic Analysis 1 (2) (1988, to appear). Zbl0683.35026MR950010
  4. [4] D. CIORANESCU, F. MURAT, Un terme étrange venu d'ailleurs, in Nonlinear partial differential equations and their applications, Collège de France Seminar, vol. II, pp. 98-138, vol. III, pp. 154-178, ed. by H. Brezis & J. L, Lions, Research Notes in Mathematics, Nos 60 & 70, Pitman, London, 1981. Zbl0496.35030
  5. [5] D. CIORANESCU, J. SAINT JEAN PAULIN, Homogenization in open sets with holes, J. Math. Anal. Appl. 71, pp. 590-607, 1979. Zbl0427.35073MR548785
  6. [6] E. DE GIORGI, T. FRANZONI, Su un tipo di convergenza variazionale, Atti.Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 58 (8), pp. 842-850, 1975. Zbl0339.49005MR448194
  7. [7] J. L. LIONS, Some methods in the mathematical analysis of Systems and their control, Science-Press, Beijing, and Gordon & Breach, NewYork, 1981. Zbl0542.93034MR664760
  8. [8] S. MORTOLA, A. PROFETI, On the convergence of the minimum points of non equicoercive quadratic functionals, Comm. in Partial Diff. Eqs. 7 (6), pp. 645-673, 1982. Zbl0489.49010MR660748
  9. [9] W. RUDIN, Real and Complex Analysis, Mc Graw-Hill, New York, 1966. Zbl0142.01701MR210528
  10. [10] E. SANCHEZ-PALENCIA, Non-homogeneous media and vibration theory, Lecture Notes in Physics, N° 127, Springer-Verlag, Berlin, 1980. Zbl0432.70002MR578345
  11. [11] L. TARTAR, Problèmes d'homogénéisation dans les équations aux dérivées partielles, Cours Peccot, Collège de France, mars 1977 (Cours partiellement rédigé dans : F. Murât, H-Convergence, Séminaire d'Analyse Fonctionnelle et Numérique, 1977/78, Université d'Alger). 

Citations in EuDML Documents

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  1. Tiziana Durante, Omogeneizzazione e fenomeno di Lavrentieff per funzionali ad andamento non standard
  2. Ciro D'Apice, Su alcune questioni di omogeneizzazione: formule di rappresentazione, domini perforati, funzionali non limitati
  3. Luisa Faella, Su alcuni problemi nell’omogeneizzazione e risultati di estensione unica nel calcolo delle variazioni
  4. Alain Damlamian, Patrizia Donato, Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?
  5. Jean Louis Woukeng, Σ -convergence of nonlinear monotone operators in perforated domains with holes of small size
  6. Alain Damlamian, Patrizia Donato, Which sequences of holes are admissible for periodic homogenization with Neumann boundary condition?
  7. Carlos Conca, François Murat, Claudia Timofte, A generalized strange term in Signorini’s type problems
  8. Carlos Conca, François Murat, Claudia Timofte, A Generalized Strange Term in Signorini's Type Problems
  9. Ciro D'Apice, Umberto De Maio, Peter I. Kogut, Suboptimal boundary controls for elliptic equation in critically perforated domain

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