Open Access
Issue
ITM Web Conf.
Volume 20, 2018
International Conference on Mathematics (ICM 2018) Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics
Article Number 02011
Number of page(s) 5
Section Numerical and Applied Analysis
DOI https://doi.org/10.1051/itmconf/20182002011
Published online 12 October 2018
  1. Olivier Alvarez and Martino Bardi. Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations. Mem. Amer. Math. Soc., 204(960):vi+77, 2010. [Google Scholar]
  2. M. Arisawa and P.-L. Lions. On ergodic stochastic control. Comm. Partial Differential Equations, 23(11-12):2187–2217, 1998. [CrossRef] [Google Scholar]
  3. G. Barles. Interior gradient bounds for the mean curvature equation by viscosity solutions methods. Differential Integral Equations, 4(2):263–275, 1991. [Google Scholar]
  4. G. Barles. A weak Bernstein method for fully nonlinear elliptic equations. Differential Integral Equations, 4(2):241–262, 1991. [Google Scholar]
  5. G. Barles. C0,α-regularity and estimates for solutions of elliptic and parabolic equations by the Ishii & Lions method. In International Conference for the 25th Anniversary of Viscosity Solutions, volume 30 of Gakuto International Series, Mathematical Sciences and Applications, pages 33–47. Gakkotosho, Tokyo, Japan, 2008. [Google Scholar]
  6. G. Barles. A short proof of the C0,α-regularity of viscosity subsolutions for superquadratic viscous Hamilton-Jacobi equations and applications. Nonlinear Anal., 73(1):31–47, 2010. [CrossRef] [Google Scholar]
  7. G. Barles. Local Gradient Estimates for Second-Order Nonlinear Elliptic and Parabolic Equations by the Weak Bernstein’s Method. Submitted. [Google Scholar]
  8. G. Barles and P. E. Souganidis. Space-time periodic solutions and long-time behavior of solutions to quasi-linear parabolic equations. SIAM J. Math. Anal., 32(6):1311–1323 (electronic), 2001. [CrossRef] [MathSciNet] [Google Scholar]
  9. Guy Barles and Francesca Da Lio. On the generalized Dirichlet problem for viscous Hamilton-Jacobi equations. J. Math. Pures Appl. (9), 83(1):53–75, 2004. [CrossRef] [Google Scholar]
  10. I. Capuzzo Dolcetta, F. Leoni, and A. Porretta. Hölder estimates for degenerate elliptic equations with coercive Hamiltonians. Trans. Amer. Math. Soc., 362(9):4511–4536, 2010. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Cardaliaguet and L. Silvestre. Hölder continuity to Hamilton-Jacobi equations with superquadratic growth in the gradient and unbounded right-hand side. Comm. Partial Differential Equations, 37(9):1668–1688, 2012. [CrossRef] [Google Scholar]
  12. 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(1):1–67, 1992. [CrossRef] [MathSciNet] [Google Scholar]
  13. F. Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Commun. Pure Appl. Anal., 3(3):395–415, 2004. [CrossRef] [Google Scholar]
  14. David Gilbarg and Neil S. Trudinger. Elliptic partial differential equations of second order. Classics in Mathematics. Springer-Verlag, Berlin, 2001. Reprint of the 1998 edition. [Google Scholar]
  15. H. Ishii and P.-L. Lions. Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. J. Differential Equations, 83(1):26–78, 1990. [CrossRef] [MathSciNet] [Google Scholar]
  16. O. Ley and V. D. Nguyen. Lipschitz regularity results for nonlinear strictly elliptic equations and applications. Journal of Differential Equations 263, 4324-4354, 2017. [CrossRef] [Google Scholar]
  17. O. Ley and V. D. Nguyen. Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems. Nonlinear Anal., 130:76–101, 2016. [CrossRef] [Google Scholar]
  18. N. V. Krylov. Lectures on elliptic and parabolic equations in Hölder spaces, volume 12 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1996. [CrossRef] [Google Scholar]
  19. P.-L. Lions. Generalized solutions of Hamilton-Jacobi equations. Pitman (Advanced Publishing Program), Boston, Mass., 1982. [Google Scholar]
  20. P.-L. Lions, B. Papanicolaou, and S. R. S. Varadhan. Homogenization of Hamilton- Jacobi equations. Unpublished, 1986. [Google Scholar]
  21. V. D. Nguyen. Regularity results and long time behavior for solutions of p-laplace equations. In preparation. [Google Scholar]

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