Homogenization of renormalized solutions of elliptic equations

François Murat

Annales de l'I.H.P. Analyse non linéaire (1991)

  • Volume: 8, Issue: 3-4, page 309-332
  • ISSN: 0294-1449

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Murat, François. "Homogenization of renormalized solutions of elliptic equations." Annales de l'I.H.P. Analyse non linéaire 8.3-4 (1991): 309-332. <http://eudml.org/doc/78256>.

@article{Murat1991,
author = {Murat, François},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {weak convergence},
language = {eng},
number = {3-4},
pages = {309-332},
publisher = {Gauthier-Villars},
title = {Homogenization of renormalized solutions of elliptic equations},
url = {http://eudml.org/doc/78256},
volume = {8},
year = {1991},
}

TY - JOUR
AU - Murat, François
TI - Homogenization of renormalized solutions of elliptic equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1991
PB - Gauthier-Villars
VL - 8
IS - 3-4
SP - 309
EP - 332
LA - eng
KW - weak convergence
UR - http://eudml.org/doc/78256
ER -

References

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  1. [BeBM 1] A. Bensoussan, L. Boccardo and F. Murat, On a Nonlinear Partial Differential Equation Having Natural Growth Terms and Unbounded Solution, Ann. Inst. Henri Poincaré, Analyse non linéaire, Vol. 5, 1988, pp. 347-364. Zbl0696.35042MR963104
  2. [BeBM 2] A. Bensoussan, L. Boccardo and F. Murat, H-Convergence for Quasilinear Elliptic Equations with Quadratic Growth, (to appear). Zbl0795.35008
  3. [BeLiP] A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978. Zbl0404.35001MR503330
  4. [B] L. Boccardo, Homogénéisation pour une classe d'équations fortement non linéaires, C. R. Acad. Sci. Paris, T 306, Serie I, 1988, pp. 253-256. Zbl0682.35034MR932331
  5. [BDGM 1] L. Boccardo, J.I. Diaz, D. Giachetti and F. Murat, Existence of a Solution for a Weaker Form of a Nonlinear Elliptic Equation, in Recent Advances in Nonlinear Elliptic and Parabolic Problems, Proceedings, Nancy, 1988, P. BENILAN, M. CHIPOT, L. C. EVANS and M. PIERRE Eds., Pitman Res. Notes in Math., Vol. 208, Longman, Harlow, 1989, pp. 229-246. Zbl0703.35063MR1035010
  6. [BDGM 2] L. Boccardo, J.I. Diaz, D. Giachetti and F. Murat, Existence and Regularity of a Renormalized Solution for Some Elliptic Problem Involving Derivatives of Nonlinear Terms, (to appear). Zbl0803.35046
  7. [BrFM] S. Brahim-Otsmane, G.A. Francfort and F. Murat, Correctors for the Homogenization of the Wave and Heat Equations, J. Math. pures et appl., (to appear). Zbl0837.35016MR1172450
  8. [DL 1] R.J. Diperna and P.-L. Lions, On the Cauchy Problem for Boltzmann Equation : Global Existence and Weak Stability, Annals of Math., Vol. 130, 1989, pp. 321-366. Zbl0698.45010MR1014927
  9. [DL2] R.J. Diperna and P.-L. Lions, On the Fokker-Planck-Boltzmann Equation, Comm. Math. Phys., Vol. 120, 1988, pp. 1-23. Zbl0671.35068MR972541
  10. [Me] N.G. Meyers, An Lp-Estimate for the Gradient of Solutions of Second Order Elliptic Divergence Equations, Ann. Sc. Norm. Sup. Pisa, Vol. 17, 1963, pp. 183- 206. Zbl0127.31904MR159110
  11. [M1] F. Murat, H-convergence, Séminaire d'analyse fonctionnelle et numérique, Université d'Alger, 1977-1978, multigraphed. 
  12. [M 2] F. Murat, A Survey on Compensated Compactness, in Contributions to Modern Calculus of Variations, L. CESARI Ed., Pitman Res. Notes in Math., Vol. 148, Longman, Harlow, 1987, pp. 145-183. MR894077
  13. [Sa] E. Sanchez-Palencia, Non Homogeneous Media and Vibration Theory, Lecture Notes in Phys., Vol. 127, Springer-Verlag, Berlin, 1980. Zbl0432.70002MR578345
  14. [S] S. Spagnolo, Sulla convergenza di soluzioni di equazioni paraboliche ed ellitiche, Ann. Sc. Norm. Sup. Pisa, Vol. 22, 1968, pp. 577-597. Zbl0174.42101MR240443
  15. [T1] L. Tartar, Cours Peccot, Collège de France, 1977. 
  16. [T2] L. Tartar, Compensated Compactness and Applications to Partial Differential Equations, in Nonlinear Analysis and Mechanics, Heriot-Watt Symposium Volume IV, R. J. KNOPS Ed., Res. Notes in Math., Vol. 39, Pitman, London, 1979, pp. 136-212. Zbl0437.35004MR584398
  17. [ZKON] V.V. Zhikov, S.M. Kozlov, O.A. Oleinik and K.T. Ngoan, Averaging and G-Convergence of Differential Operators, Russian Math. Surveys, Vol. 34, 1979, pp. 39-147. Zbl0445.35096MR562800

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