Homogenization of periodic semilinear hypoelliptic PDEs
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 2, p. 253-283

We establish homogenization results for both linear and semilinear partial differential equations of parabolic type, when the linear second order PDE operator satisfies a hypoellipticity asumption, rather than the usual ellipticity condition. Our method of proof is essentially probabilistic.

Nous établissons des résultats d’homogénéisation d’équations aux dérivées partielles paraboliques linéaires et semi–linéaires, sous une hypothèse d’hypoellipticité de l’opérateur aux dérivées partielles du second ordre, au lieu de l’hypothèse usuelle d’ellipticité. Notre méthode de démonstration est essentiellement probabiliste.

@article{AFST_2007_6_16_2_253_0,
     author = {Di\'edhiou, Alassane and Pardoux, \'Etienne},
     title = {Homogenization of periodic semilinear hypoelliptic PDEs},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 16},
     number = {2},
     year = {2007},
     pages = {253-283},
     doi = {10.5802/afst.1148},
     mrnumber = {2331541},
     zbl = {1131.35304},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2007_6_16_2_253_0}
}
Diédhiou, Alassane; Pardoux, Étienne. Homogenization of periodic semilinear hypoelliptic PDEs. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 16 (2007) no. 2, pp. 253-283. doi : 10.5802/afst.1148. http://www.numdam.org/item/AFST_2007_6_16_2_253_0/

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