Long time averaged reflection force and homogenization of oscillating Neumann boundary conditions
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 2, p. 293-332
@article{AIHPC_2003__20_2_293_0,
     author = {Arisawa, Mariko},
     title = {Long time averaged reflection force and homogenization of oscillating Neumann boundary conditions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {20},
     number = {2},
     year = {2003},
     pages = {293-332},
     doi = {10.1016/S0294-1449(02)00025-2},
     zbl = {01912452},
     mrnumber = {1961518},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2003__20_2_293_0}
}
Arisawa, Mariko. Long time averaged reflection force and homogenization of oscillating Neumann boundary conditions. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 2, pp. 293-332. doi : 10.1016/S0294-1449(02)00025-2. http://www.numdam.org/item/AIHPC_2003__20_2_293_0/

[1] Arisawa M., Ergodic problem for the Hamilton-Jacobi-Bellman equations I, Existence of the ergodic attractor, Ann. IHP Anal. Non Lineaire 14 (1997) 415-438. | Numdam | MR 1464529 | Zbl 0892.49015

[2] Arisawa M., Ergodic problem for the Hamilton-Jacobi equations II, Ann. IHP Anal. Non Linearire 15 (1998) 1-24. | Numdam | MR 1614615 | Zbl 0903.49018

[3] M. Arisawa, Multiscale homogenizations for first order Hamilton-Jacobi-Bellman equations, Differential and Integral Equations, to appear. | MR 1364034

[4] M. Arisawa, Quasi-periodic homogenizations for second order Hamilton-Jacobi-Bellman equations, J. Math. Sci. Appl., to appear. | MR 1842387 | Zbl 1014.49018

[5] M. Arisawa, Y. Giga, Anisotropic curvature flows in a very thin domain, Hokkaido University Preprint Series in Mathematics 495 (2000), to appear in Indiana U. Math. J. | MR 1976078 | Zbl 1028.35076

[6] Arisawa M., Lions P.-L., On ergodic stochastic control, Comm. Partial Differential Equations 23 (11-12) (1998) 2187-2217. | MR 1662180 | Zbl 01247980

[7] Bardi M., Da Lio F., On the strong maximum principle for fully nonlinear degenerate elliptic equations, Arch. Math. 73 (4) (1999) 276-285. | MR 1710100 | Zbl 0939.35038

[8] Barles G., Nonlinear Neumann boundary conditions for quasilinear degenerate elliptic equations and applications, J. Differential Equations 154 (1999) 191-224. | MR 1685618 | Zbl 0924.35051

[9] Barles G., Perthame B., Exit time problems in optimal control and the vanishing viscosity method, SIAM J. Control Optim. 26 (1988) 1133-1148. | MR 957658 | Zbl 0674.49027

[10] Bensoussan A., Perturbation Methods in Optimal Control, Series in Modern Applied Mathematics, Wiley, Gauthier-Villars, 1988. | MR 949208 | Zbl 0648.49001

[11] Bensoussan A., Lions J.L., Papanicolaou G., Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978. | MR 503330 | Zbl 0404.35001

[12] Cabre X., Caffarelli L.A., Fully Nonlinear Elliptic Equations, AMS Colloquium Publications, 43, 1995. | MR 1351007 | Zbl 0834.35002

[13] Chechkin G., Friedman A., Piatnitski A., The boundary value problems in domains with very rapidly oscillating boundary, J. Math. Anal. Appl. 231 (1) (1999) 213-234. | MR 1676697 | Zbl 0938.35049

[14] Crandall M.G., Fok K., Kocan M., Swiech A., Remarks on nonlinear uniformly parabolic equations, Indiana Univ. Math. J. 47 (4) (1998) 1293-1326. | MR 1687138 | Zbl 0933.35091

[15] Crandall M.G., Ishii H., Lions P.-L., User's guide to viscosity solutions of second order partial differential equations, Bull. AMS 27 (1) (1992). | MR 1118699 | Zbl 0755.35015

[16] Crandall M.G., Lions P.-L., Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983) 1-42. | MR 690039 | Zbl 0599.35024

[17] Evans L.C., Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math. XXXV (1982) 333-363. | MR 649348 | Zbl 0469.35022

[18] Evans L.C., The perturbed test function method for viscosity solutions of nonlinear P.D. E's, Proc. Roy. Soc. Edinburgh 111A (1989) 359-375. | MR 1007533 | Zbl 0679.35001

[19] Evans L.C., Periodic homogeneization of certain fully nonlinear partial differential equations, Proc. Roy. Soc. Edinburgh 120A (1992) 245-265. | MR 1159184 | Zbl 0796.35011

[20] Fleming W.H., Soner H.M., Controlled Markov Processes and Viscosity Solution, Springer, New York, 1993. | MR 1199811 | Zbl 0773.60070

[21] Freidlin M.I., Wentzell A.D., Random Perturbations of Dynamical Systems, Springer-Verlag, Berlin, 1984. | MR 722136 | Zbl 0922.60006

[22] Friedman A., Hu B., Liu Y., A boundary value problem for the Poisson equation with multi-scale oscillating boundary, J. Differential Equations 137 (1997) 54-93. | MR 1451536 | Zbl 0878.35014

[23] Gilbarg D., Trudinger N.S., Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York, 1983. | MR 737190 | Zbl 0361.35003

[24] Ishii H., Lions P.-L., Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations 83 (1990) 26-78. | MR 1031377 | Zbl 0708.35031

[25] Krylov N.V., Boundary nonhomogeneous elliptic and parabolic equations, Math. USSR Izv. 20 (1983) 459-492. | Zbl 0529.35026

[26] Krylov N.V., Boundary nonhomogeneous elliptic and parabolic equations in a domain, Math. USSR Izv. 22 (1984) 67-97. | Zbl 0578.35024

[27] Lions P.-L., Neumann type boundary conditions for Hamilton-Jacobi equations, Duke J. Math. 52 (1985) 793-820. | MR 816386 | Zbl 0599.35025

[28] Lions P.-L., Menaldi J.M., Sznitman A.S., Construction de processus de diffusion reflechis par penalisation du domaine, Comptes Rendus Paris 292 (1981) 559-562. | MR 614669 | Zbl 0468.60073

[29] P.-L. Lions, G. Papanicolau, S.R.S. Varadhan, Homogeneizations of Hamilton-Jacobi equations, Preprint.

[30] Lions P.-L., Sznitman A.S., Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. 37 (1) (1984) 511-537. | MR 745330 | Zbl 0598.60060

[31] Lions P.-L., Trudinger N.S., Linear oblique derivative problems for the uniformly elliptic Hamilton-Jacobi-Bellman equation, Math. Z. 191 (1986) 1-15. | MR 812598 | Zbl 0593.35046