@article{AIHPC_2009__26_3_979_0, author = {Sow, A. B. and Rhodes, R. and Pardoux, \'e.}, title = {Homogenization of {Periodic} {Semilinear} {Parabolic} {Degenerate} {PDEs}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {979--998}, publisher = {Elsevier}, volume = {26}, number = {3}, year = {2009}, doi = {10.1016/j.anihpc.2008.09.001}, mrnumber = {2526412}, zbl = {1178.35052}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2008.09.001/} }
TY - JOUR AU - Sow, A. B. AU - Rhodes, R. AU - Pardoux, é. TI - Homogenization of Periodic Semilinear Parabolic Degenerate PDEs JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 979 EP - 998 VL - 26 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2008.09.001/ DO - 10.1016/j.anihpc.2008.09.001 LA - en ID - AIHPC_2009__26_3_979_0 ER -
%0 Journal Article %A Sow, A. B. %A Rhodes, R. %A Pardoux, é. %T Homogenization of Periodic Semilinear Parabolic Degenerate PDEs %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 979-998 %V 26 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2008.09.001/ %R 10.1016/j.anihpc.2008.09.001 %G en %F AIHPC_2009__26_3_979_0
Sow, A. B.; Rhodes, R.; Pardoux, é. Homogenization of Periodic Semilinear Parabolic Degenerate PDEs. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 3, pp. 979-998. doi : 10.1016/j.anihpc.2008.09.001. http://www.numdam.org/articles/10.1016/j.anihpc.2008.09.001/
[1] Asymptotic Analysis for Periodic Structures, North-Holland, 1978. | MR | Zbl
, , ,[2] Stability of BSDEs With Random Terminal Time and Homogenization of Semilinear Elliptic PDEs, J. Funct. Anal. 155 (1998) 455-494. | MR | Zbl
, ,[3] Probabilistic Approach to Homogenization of Viscosity Solutions of Parabolic PDEs, NoDEA Nonlinear Differential Equations Appl. 6 (4) (1999) 395-411. | MR | Zbl
, , ,[4] User's Guide to Viscosity Solutions of Second Order Partial Differential Equations, Bull. Amer. Math. Soc. 27 (1992) 1-67. | MR | Zbl
, , ,[5] On the Homogenization of Degenerate Elliptic Equations in Divergence Form, J. Math. Pures Appl. 71 (1992) 119-138. | MR | Zbl
, ,[6] On the Existence and Uniqueness of Solutions to FBSDEs in a Non-Degenerate Case, Stochastic Process. Appl. 99 (2) (2002) 209-286. | MR | Zbl
,[7] Auxiliary SDEs for Homogenization of Quasilinear PDEs With Periodic Coefficients, Ann. Probab. B 32 (3) (2004) 2305-2361. | MR | Zbl
,[8] Stochastic Homogenization of Quasilinear PDEs With a Spatial Degeneracy, Asymptot. Anal., in press, available on, http://hal.archives-ouvertes.fr/. | MR | Zbl
, ,[9] Singular Homogenization With Stationary in Time and Periodic in Space Coefficients, J. Funct. Anal. 231 (2006) 1-46. | MR | Zbl
, , , ,[10] Homogenization of Random Degenerated Nonlinear Monotone Operators, Glas. Mat. Ser. III 41 (61) (2006) 101-114. | MR | Zbl
, , , ,[11] Markov Processes, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons Inc., New York, 1986. | MR | Zbl
, ,[12] The Dirichlet Problem for an Equation With Periodic Coefficients Depending on a Small Parameter, Teor. Veroyatnost. i Primenen. 9 (1964) 133-139. | MR | Zbl
,[13] Homogenization of Periodic Linear Degenerate PDEs, available on, arXiv: math/0702304v1. | MR | Zbl
, ,[14] H-Convergence and Regular Limits for Stratified Media With Low and High Conductivities, Appl. Anal. 57 (3-4) (1995) 271-308. | MR | Zbl
, ,[15] Homogenization of Degenerate Quasilinear Parabolic Equations With Periodic Structure, Asymptotic Anal. 48 (2006) 77-89. | MR | Zbl
, , ,[16] Continuous Dependence Estimates for Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Equations, J. Differential Equations 183 (2002) 497-525. | MR | Zbl
, ,[17] A. Lejay, Méthodes probabilistes pour l'homogénéisation des opérateurs sous forme divergence, Thèse de l'université de Provence, 2000.
[18] Tightness Criteria for Laws of Semartingales, Ann. Inst. Henri Poincaré 20 (1984) 353-372. | Numdam | MR | Zbl
, ,[19] Homogenization of a Linear and Semilinear Second Order Parabolic PDEs With Periodic Coefficients: a Probabilistic Approach, J. Funct. Anal. 167 (1999) 498-520. | MR | Zbl
,[20] BSDEs, Weak Convergence and Homogenization of Semilinear PDEs, in: , (Eds.), Nonlinear Analysis, Differential Equations and Control, Kluwer Acad. Publ., 1999, pp. 503-549. | MR | Zbl
,[21] Backward Stochastic Differential Equations and Viscosity Solutions of Systems of Semilinear Parabolic and Elliptic PDEs of Second Order, in: , , , (Eds.), Stochastic Analysis and Related Topics VI: the Geilo Workshop, 1996, Birkhäuser, 1998, pp. 79-127. | MR | Zbl
,[22] Backward Stochastic Differential Equations and Quasilinear Parabolic Partial Differential Equations, in: , (Eds.), Stochastic Partial Differential Equations and Their Applications, Lecture Notes in Control & Information Sciences, vol. 176, Springer, Berlin, 1992, pp. 200-217. | MR | Zbl
, ,[23] Averaging of Backward Stochastic Differential Equations With Application to Semilinear PDE's, Stochastics Stochastic Rep. 60 (1997) 255-270. | MR | Zbl
, ,[24] On Poisson Equation and Diffusion Approximation 1, Ann. Probab. 29 (2001) 1061-1085. | MR | Zbl
, ,[25] On Poisson Equation and Diffusion Approximation 3, Ann. Probab. 33 (2005). | MR | Zbl
, ,[26] On the Convergence of a Class of Degenerate Parabolic Equations, J. Math. Pures Appl. 77 (1998) 851-878. | MR | Zbl
, ,[27] Homogenization of a Class of Degenerate Parabolic Equations, Asymptotic Anal. 21 (1999) 275-302. | MR | Zbl
,[28] Homogenization of Degenerate Elliptic-Parabolic Equations, Asymptotic Anal. 37 (2004) 21-56. | MR | Zbl
,[29] On Homogenization of Space-Time Dependent and Degenerate Random Flows, Stochastic Process. Appl. 117 (2007) 1561-1585. | MR | Zbl
,[30] R. Rhodes, Homogenization of locally ergodic diffusions with possibly degenerate diffusion matrix, Ann. Inst. H. Poincaré Probab. Statist., in press.
Cité par Sources :