Free Access
Volume 22, Number 3, July-September 2016
Page(s) 842 - 861
Published online 16 June 2016
  1. O. Alvarez and M. Bardi, Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations. Mem. Amer. Math. Soc. 204 (2010) 960. [Google Scholar]
  2. A. Arapostathis, V.S. Borkar and M.K. Ghosh, Ergodic control of diffusion processes. Cambridge University Press, Cambridge (2012). [Google Scholar]
  3. M. Arisawa and P.-L. Lions, On ergodic stochastic control. Commun. Partial Differ. Equ. 23 (1998) 2187–2217. [Google Scholar]
  4. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton−Jacobi−Bellman equations. Birkhäuser Boston, Boston, MA (1997). [Google Scholar]
  5. M. Bardi and P. Goatin, Invariant sets for controlled degenerate diffusions: a viscosity solutions approach, in “Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming”, edited by W.M. McEneaney, G.G. Yin and Q. Zhang. Birkhäuser, Boston (1999) 191–208. [Google Scholar]
  6. M. Bardi and F. Da Lio, Propagation of maxima and strong maximum principle for fully nonlinear degenerate elliptic equations. Part I: convex operators. Nonlinear Anal. 44 (2001) 991–1006. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Bardi and R. Jensen, A geometric characterization of viable sets for controlled degenerate diffusions. Set-Valued Anal. 10 (2002) 129–141. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Bardi and F. Da Lio, Propagation of maxima and strong maximum principle for fully nonlinear degenerate elliptic equations. Part II: concave operators. Indiana Univ. Math. J. 52 (2003) 607–627. [CrossRef] [MathSciNet] [Google Scholar]
  9. G. Barles, Fully nonlinear Neumann type boundary conditions for second-order elliptic and parabolic equations. J. Differ. Equ. 106 (1993) 90–106. [CrossRef] [Google Scholar]
  10. G. Barles and J. Burdeau, The Dirichlet problem for semilinear second-order degenerate elliptic equations and applications to stochastic exit time control problems. Commun. Partial Differ. Eq. 20 (1995) 129–178. [CrossRef] [Google Scholar]
  11. G. Barles and E. Rouy, A strong comparison result for the Bellman equation arising in stochastic exit time control problems and its applications. Commun. Partial Differ. Equ. 23 (1998) 11–12, 1995–2033. [CrossRef] [Google Scholar]
  12. G. Barles and F. Da Lio, On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions. Ann. Inst. Henri Poincaré Anal. Non Linéaire 22 (2005) 521–541. [CrossRef] [Google Scholar]
  13. G. Barles, A. Porretta and T.T. Tchamba, On the large time behavior of solutions of the Dirichlet problem for subquadratic viscous Hamilton-Jacobi equations. J. Math. Pures Appl. 94 (2010) 497–519. [CrossRef] [MathSciNet] [Google Scholar]
  14. A. Bensoussan and J. Frehse, Ergodic control Bellman equation with Neumann boundary conditions. Vol. 280 of Lect. Notes Control Inform. Sci. Springer, Berlin (2002) 59–71. [Google Scholar]
  15. H. Berestycki, I. Capuzzo Dolcetta, A. Porretta, L. Rossi, Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators. J. Math. Pures Appl. 103 (2015) 1276–1293. [CrossRef] [MathSciNet] [Google Scholar]
  16. V. Borkar and A. Budhiraja, Ergodic control for constrained diffusions: characterization using HJB equations. SIAM J. Control Optim. 43 (2004/05) 1467–1492. [CrossRef] [MathSciNet] [Google Scholar]
  17. P. Cannarsa, G. Da Prato and H. Frankowska, Invariant measures associated to degenerate elliptic operators. Indiana Univ. Math. J. 59 (2010) 53–78. [CrossRef] [MathSciNet] [Google Scholar]
  18. I. Capuzzo Dolcetta, A. Cutrì, Hadamard and Liouville type results for fully nonlinear partial differential inequalities. Commun. Contemp. Math. 5 (2003) 435–448. [CrossRef] [MathSciNet] [Google Scholar]
  19. A. Cesaroni, Lyapunov Stabilizability of Controlled Diffusions via a Superoptimality Principle for Viscosity Solutions. Appl. Math. Optim. 53 (2006) 1–29. [CrossRef] [MathSciNet] [Google Scholar]
  20. H. Chen and P. Felmer, On Liouville type theorems for fully nonlinear elliptic equations with gradient term. J. Differ. Eq. 255 (2013) 2167–2195. [CrossRef] [Google Scholar]
  21. M.G. Crandall, H. Ishii and P.-L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 (1992) 1–67. [Google Scholar]
  22. G. Fichera, Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine. Atti Accad. Naz. Lincei. Mem. Cl. Sci. Fis. Mat. Nat. Sez. I. 5 (1956) 1–30. [MathSciNet] [Google Scholar]
  23. W.H. Fleming and H.M. Soner, Controlled Markov processes and viscosity solutions. 2nd edition. Springer, New York (2006). [Google Scholar]
  24. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer, Berlin (1988). [Google Scholar]
  25. U.G. Haussmann and J.-P. Lepeltier, On the existence of optimal controls. SIAM J. Control Optim. 28 (1990) 851–902. [CrossRef] [MathSciNet] [Google Scholar]
  26. J.M. Lasry and P.-L. Lions, Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. I. The model problem. Math. Ann. 283 (1989) 583–630. [CrossRef] [MathSciNet] [Google Scholar]
  27. T. Leonori and A. Porretta, Gradient bounds for elliptic problems singular at the boundary. Arch. Ration. Mech. Anal. 202 (2011) 663–705. [CrossRef] [MathSciNet] [Google Scholar]
  28. P.-L. Lions, Quelques remarques sur les problèmes elliptiques quasilinéaires du second ordre. J. Anal. Math. 45 (1985) 234–254. [CrossRef] [Google Scholar]
  29. P.-L. Lions and C. Villani, Régularité optimale de racines carrées. C. R. Acad. Sci. Paris Sér. I Math. 321 (1995) 1537–1541. [Google Scholar]
  30. A. Porretta, The “ergodic limit” for a viscous Hamilton-Jacobi equation with Dirichlet conditions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 21 (2010) 59–78. [CrossRef] [MathSciNet] [Google Scholar]
  31. M.V. Safonov, On the classical solution of Bellman’s elliptic equation. Sov. Math. Dokl. 30 (1984) 482–485. [Google Scholar]
  32. N.S. Trudinger, On regularity and existence of viscosity solutions of nonlinear second order, elliptic equations. Partial differential equations and the calculus of variations. Vol. II of Progr. Nonlin. Differ. Equ. Appl. Birkhäuser Boston, Boston, MA (1989) 939–957. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.