Stochastic homogenization of level-set convex Hamilton-Jacobi equations

International Mathematics Research Notices

Volumn 2013, Issue 15, 2013, Pages 3420-3449

  Armstrong, Scott N ^a   Souganidis, Panagiotis E ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84881184359     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1093/imrn/rns155     Document Type: Article

References (29)

1. Akcoglu, M. A. and U. Krengel. "Ergodic theorems for superadditive processes." Journal fü r die Reine und Angewandte Mathematik 323 (1981): 53-67
2. Armstrong, S. N. and P. E. "Souganidis. Stochastic homogenization of L∞ variational problems." Advances in Mathematics 2289, no. 6 (2012): 3508-35
3. Armstrong, S. N. and P. E. Souganidis. "Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments." Journal de Math́ematiques Pures et Appliqúees 97, no. 5 (2012), 460-504
4. Barles, G. Solutions de Viscosité des Équations de Hamilton-Jacobi. Mathématiques & Applications (Berlin) [Mathematics & Applications] 17. Paris: Springer, 1994
5. Becker, M. E. "Multiparameter groups of measure-preserving transformations: A simple proof of Wiener's ergodic theorem." The Annals of Probability 9, no. 3 (1981): 504-9
6. Concordel, M. C. "Periodic homogenisation of Hamilton-Jacobi equations. II. Eikonal equations." Proceedings of the Royal Society of Edinburgh. Section A 127, no. 4 (1997): 665-89
7. Crandall, M. G., H. Ishii, and P-L. Lions. "User's guide to viscosity solutions of second order partial differential equations." Bulletin of the American Mathematical Society (New Series)27, no. 1 (1992): 1-67
8. Davini, A. and A. Siconolfi. "Exact and approximate correctors for stochastic Hamiltonians: The 1-dimensional case." Mathematische Annalen 345, no. 4 (2009): 749-82
9. Davini, A. and A. Siconolfi. "Metric techniques for convex stationary ergodic Hamiltonians." Calculus of Variations and Partial Differential Equations, 40, no. 3-4 (2011): 391-421
10. Davini, A. and A. Siconolfi. "Weak KAM Theory topics in the stationary ergodic setting." Calculus of Variations and Partial Differential Equations, in Press
11. E, W. Aubry-Mather theory and periodic solutions of the forced Burgers equation. Communications on Pure and Applied Mathematics 52, no. 7 (1999): 811-28
12. Evans, L. C. "Periodic homogenisation of certain fully nonlinear partial differential equations." Proceedings of the Royal Society of Edinburgh. Section A 120, no. 3-4 (1992): 245-65
13. Evans, L. C. and D. Gomes. "Effective Hamiltonians and averaging for Hamiltonian dynamics. I." Archive for Rational Mechanics and Analysis 157, no. 1 (2001): 1-33
14. Ishii, H. "Almost Periodic Homogenization of Hamilton-Jacobi Equations." In International Conference on Differential Equations, vols. 1, 2 (Berlin, 1999), 600-05. River Edge, NJ:World Scientific Publisher, 2000
15. Kosygina, E., F. Rezakhanlou, and S. R. S. Varadhan. "Stochastic homogenization of Hamilton-Jacobi-Bellman equations." Communications on Pure and Applied Mathematics 59, no. 10 (2006): 1489-521
16. Kosygina, E. and S. R. S. Varadhan. "Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium." Communications on Pure and Applied Mathematics 61, no. 6 (2008): 816-47
17. Kozlov, S. M. "The averaging method and walks in inhomogeneous environments." Uspekhi Matematicheskikh Nauk 40 no. 2(242) (1985): 61-120, 238
18. Lions, P-L. Generalized Solutions of Hamilton-Jacobi Equations. Research Notes in Mathematics 69. Boston, MA: Pitman (Advanced Publishing Program), 1982
19. Lions, P-L., G. C. Papanicolaou, and S. R. S. Varadhan. "Homogenization of Hamilton-Jacobi equations." Unpublished preprint, 1987
20. Lions, P-L. and P. E. Souganidis. Personal communication
21. Lions, P-L. and P. E. Souganidis. "Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting." Communications on Pure and Applied Mathematics 56, no. 10 (2003): 1501-24
22. Lions, P-L. and P. E. Souganidis. "Homogenization of 'viscous' Hamilton-Jacobi equations in stationary ergodic media." Communications in Partial Differential Equations 30, no. 1-3 (2005): 335-75
23. Lions, P-L. and P. E. Souganidis. "Stochastic homogenization of Hamilton-Jacobi and 'viscous'-Hamilton-Jacobi equations with convex nonlinearities -revisited." Communications in Mathematical Sciences 8, no. 2 (2010): 627-37
24. Rezakhanlou, F. and J. E. Tarver. "Homogenization for stochastic Hamilton-Jacobi equations." Archive for Rational Mechanics and Analysis 151, no. 4 (2000): 277-309
25. Schwab, R. W. "Stochastic homogenization of Hamilton-Jacobi equations in stationary ergodic spatio-Temporal media." Indiana University Mathematics Journal 58, no. 2 (2009): 537-81
26. Souganidis, P. E. "Stochastic homogenization of Hamilton-Jacobi equations and some applications." Asymptotic Analysis 20, no. 1 (1999): 1-11
27. Sznitman, A-S. Brownian Motion, Obstacles and Random Media. Springer Monographs in Mathematics. Berlin: Springer, 1998
28. Oberman, A.M., Takei, R. and T. Vladimirsky. "Homogenization of metric Hamilton-Jacobi equations." Multiscale Modeling Simulation 8, no. 1 (2009): 269-95
29. Luo, S., Yu, Y. and H. Zhou. "A new approximation for effective Hamiltonians for homogenization of a class of Hamilton-Jacobi equations." Multiscale Modeling Simulation 9, no. 2 (2011): 711-34