Free Access
Issue |
ESAIM: COCV
Volume 27, 2021
|
|
---|---|---|
Article Number | 68 | |
Number of page(s) | 33 | |
DOI | https://doi.org/10.1051/cocv/2021023 | |
Published online | 28 June 2021 |
- S. Armstrong, P. Cardaliaguet and P. Souganidis, Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations. J. Amer. Math. Soc. 27 (2014) 479–540. [CrossRef] [Google Scholar]
- J. Ball and V.J. Mizel, One-dimensional Variational Problems whose Minimizers do not Satisfy the Euler-Lagrange Equation. Arch. Ratl. Mech. Anal. 90 (1985) 325–388. [CrossRef] [Google Scholar]
- A. Davini and A. Siconolfi, Metric techniques for convex stationary ergodic Hamiltonians. Calc. Variat. Partial Differ. Equ. 40 (2011) 391–421. [CrossRef] [Google Scholar]
- A. Davini and A. Siconolfi, Weak KAM theory topics in the stationary ergodic setting. Calc. Variat. Partial Differ. Equ. 44 (2012) 319–350. [CrossRef] [Google Scholar]
- N. Dirr, F. Dragoni, P. Mannucci and C. Marchi, Stochastic homogenization for functionals with anisotropic rescaling and noncoercive Hamilton–Jacobi equations. SIAM J. Math. Anal. 50 (2018) 5198–5242. [CrossRef] [Google Scholar]
- L.C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE. Proc. Royal Soc. Edinburgh: Sect. A Math. 111 (1989) 359–375. [CrossRef] [MathSciNet] [Google Scholar]
- W.M. Feldman and P.E. Souganidis, Homogenization and non-homogenization of certain non-convex Hamilton-Jacobi equations. J. Math. Pures Appl. 108 (2017) 751–782. [CrossRef] [Google Scholar]
- A. Filippov, On certain questions in the theory of optimal control. J. Soc. Ind. Appl. Math. Ser. A Control 1 (1962) 76–84. [CrossRef] [Google Scholar]
- W. Fleming and H. Soner, Controlled Markov Processes and Viscosity Solutions Stochastic Modelling and Applied Probability, Springer New York (2006). [Google Scholar]
- H. Ishii, Almost periodic homogenization of Hamilton-Jacobi equations. Int. Conf. Differ. Equ. 1 (2000). [Google Scholar]
- W. Jing, P.E. Souganidis and H.V. Tran, Stochastic homogenization of viscous superquadratic Hamilton–Jacobi equations in dynamic random environment. Res. Math. Sci. 4 (2017) 6. [Google Scholar]
- E. Kosygina, F. Rezakhanlou and S.R.S. Varadhan, Stochastic homogenization of Hamilton-Jacobi-Bellman equations. Commun. Pure Appl. Math. 59 (2006) 1489–1521. [Google Scholar]
- U. Krengel and A. Brunel, Ergodic Theorems. De Gruyter Studies in Mathematics, De Gruyter (1985). [Google Scholar]
- P.-L. Lions, G. Papanicolaou and S.R. Varadhan, Homogenization of Hamilton-Jacobi equations. unpublished (1986). [Google Scholar]
- P.-L. Lions and P. Souganidis, Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting. Commun. Pure Appl. Math. 56 (2003) 1501–1524. [Google Scholar]
- P.-L. Lions and P.E. Souganidis, Homogenization of “viscous” Hamilton–Jacobi equations in stationary ergodic media. Commun. Partial Differ. Equ. 30 (2005) 335–375. [Google Scholar]
- F. Rezakhanlou and J.E. Tarver, Homogenization for stochastic Hamilton-Jacobi equations. Arch. Ratl. Mech. Anal. 151 (2000) 277–309. [Google Scholar]
- E. Roxin, The existence of optimal controls. Michigan Math. J. 9 (1962) 109–119. [Google Scholar]
- H. Royden, Real Analysis. Mathematics and statistics, Macmillan (1988). [Google Scholar]
- P.E. Souganidis, Stochastic homogenization of Hamilton–Jacobi equations and some applications. Asymptotic Anal. 20 (1999) 1–11. [Google Scholar]
- A. Stoddart, Existence of optimal controls. Pacific J. Math. 20 (1967) 167–177. [Google Scholar]
- B. Ziliotto, Stochastic Homogenization of Nonconvex Hamilton-Jacobi Equations: A Counterexample. Commun. Pure Appl. Math. (2015) arXiv:1512.06375.. [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.