@article{AIHPC_2005__22_5_521_0, author = {Barles, Guy and Da Lio, Francesca}, title = {On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear {Neumann} boundary conditions}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {521--541}, publisher = {Elsevier}, volume = {22}, number = {5}, year = {2005}, doi = {10.1016/j.anihpc.2004.09.001}, mrnumber = {2171989}, zbl = {02235966}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2004.09.001/} }
TY - JOUR AU - Barles, Guy AU - Da Lio, Francesca TI - On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions JO - Annales de l'I.H.P. Analyse non linéaire PY - 2005 SP - 521 EP - 541 VL - 22 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2004.09.001/ DO - 10.1016/j.anihpc.2004.09.001 LA - en ID - AIHPC_2005__22_5_521_0 ER -
%0 Journal Article %A Barles, Guy %A Da Lio, Francesca %T On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions %J Annales de l'I.H.P. Analyse non linéaire %D 2005 %P 521-541 %V 22 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2004.09.001/ %R 10.1016/j.anihpc.2004.09.001 %G en %F AIHPC_2005__22_5_521_0
Barles, Guy; Da Lio, Francesca. On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions. Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 5, pp. 521-541. doi : 10.1016/j.anihpc.2004.09.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2004.09.001/
[1] Viscosity solutions methods for singular perturbations in deterministic and stochastic control, SIAM J. Control Optim. 40 (4) (2001/02) 1159-1188. | MR | Zbl
, ,[2] Singular perturbations of nonlinear degenerate parabolic PDEs: a general convergence result, Arch. Rational Mech. Anal. 170 (1) (2003) 17-61. | MR | Zbl
, ,[3] Ergodic problem for the Hamilton-Jacobi-Bellman equation. I. Existence of the ergodic attractor, Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (4) (1997) 415-438. | EuDML | Numdam | MR | Zbl
,[4] Ergodic problem for the Hamilton-Jacobi-Bellman equation. II, Ann. Inst. Poincaré Anal. Non Linéaire 15 (1) (1998) 1-24. | EuDML | Numdam | MR | Zbl
,[5] Long time averaged reflection force and homogenization of oscillating Neumann boundary conditions, Ann. Inst. H. Poincaré Anal. Linéaire 20 (2) (2003) 293-332. | EuDML | Numdam | MR | Zbl
,[6] On ergodic stochastic control, Comm. Partial Differential Equations 23 (11-12) (1998) 2187-2217. | MR | Zbl
, ,[7] A viscosity solutions approach to some asymptotic problems in optimal control, in: Partial Differential Equation Methods in Control and Shape Analysis (Pisa), Lecture Notes in Pure and Appl. Math., vol. 188, Dekker, New York, 1997, pp. 29-39. | MR | Zbl
, , ,[8] On the strong maximum principle for fully nonlinear degenerate elliptic equations, Arch. Math. (Basel) 73 (4) (1999) 276-285. | MR | Zbl
, ,[9] Nonlinear Neumann boundary conditions for quasilinear degenerate elliptic equations and applications, J. Differential Equations 154 (1999) 191-224. | MR | Zbl
,[10] G. Barles, F. Da Lio, Local estimates for viscosity solutions of Neumann-type boundary value problems, preprint. | MR
[11] Remarques sur les problèmes de riflexion obliques, C. R. Acad. Sci. Paris, Ser. I 320 (1995) 69-74. | MR | Zbl
, ,[12] G. Barles, M. Ramaswamy, Sufficient structure conditions for uniqueness of viscosity solutions of semilinear and quasilinear equations, NoDEA, in press. | MR | Zbl
[13] On the large time behaviour of solutions of Hamilton-Jacobi equations, SIAM J. Math. Anal. 31 (4) (2000) 925-939. | MR | Zbl
, ,[14] Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations, SIAM J. Math. Anal. 32 (6) (2001) 1311-1323. | MR | Zbl
, ,[15] Perturbation methods in optimal control, Wiley/Gauthier-Villars Series in Modern Applied Mathematics, Wiley, Chichester, 1988, Translated from the French by C. Tomson. | MR | Zbl
,[16] On Bellman equations of ergodic control in , J. Reine Angew. Math. 429 (1992) 125-160. | MR | Zbl
, ,[17] Ergodic control Bellman equation with Neumann boundary conditions, in: Stochastic Theory and Control (Lawrence, KS, 2001), Lecture Notes in Control and Inform. Sci., vol. 280, Springer, Berlin, 2002, pp. 59-71. | MR | Zbl
, ,[18] Hamilton-Jacobi equations with state constraints, Trans. Amer. Math. Soc. 318 (2) (1990) 643-683. | MR | Zbl
, ,[19] Periodic homogenization of Hamilton-Jacobi equations: additive eigenvalues and variational formula, Indiana Univ. Math. J. 45 (4) (1996) 1095-1117. | MR | Zbl
,[20] Periodic homogenization of Hamilton-Jacobi equations: II: Eikonal equations, Proc. Roy. Soc. Edinburgh Sect. A 127 (4) (1997) 665-689. | MR | Zbl
,[21] User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Soc. 27 (1992) 1-67. | MR | Zbl
, , ,[22] The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Roy. Soc. Edinburgh Sect. A 111 (3-4) (1989) 359-375. | MR | Zbl
,[23] Periodic homogenisation of certain fully nonlinear partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A 120 (3-4) (1992) 245-265. | MR | Zbl
,[24] Effective Hamiltonians and averaging for Hamiltonian dynamics. I., Arch. Rational Mech. Anal. 157 (1) (2001) 1-33. | MR | Zbl
, ,[25] Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens, C. R. Acad. Sci. Paris, Sér. I Math. 324 (1997) 1043-1046. | MR | Zbl
,[26] Solutions KAM faibles conjuguées et barrières de Peierls, C. R. Acad. Sci. Paris, Sér. I Math. 325 (6) (1997) 649-652. | MR | Zbl
,[27] Sur la convergence du semi-groupe de Lax-Oleinik, C. R. Acad. Sci. Paris, Sér. I Math. 327 (3) (1998) 267-270. | MR | Zbl
,[28] Almost periodic homogenization of Hamilton-Jacobi equations, in: International Conference on Differential Equations, vols. 1, 2 (Berlin, 1999), World Sci., River Edge, NJ, 2000, pp. 600-605. | MR | Zbl
,[29] Perron's method for Hamilton-Jacobi equations, Duke Math. J. 55 (1987) 369-384. | MR | Zbl
,[30] Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints, Math. Ann. 283 (1989) 583-630. | MR | Zbl
, ,[31] Neumann type boundary conditions for Hamilton-Jacobi equations, Duke Math. J. 52 (4) (1985) 793-820. | MR | Zbl
,[32] P.-L. Lions, G. Papanicolaou, S.R.S Varadhan, unpublished preprint.
[33] Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math. XXXVII (1984) 511-537. | MR | Zbl
, ,[34] Remarks on the long time behaviour of the solutions of Hamilton-Jacobi equations, Comm. Partial Differential Equations 24 (5-6) (1999) 883-893. | MR | Zbl
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