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All issues Volume 27 (2021) ESAIM: COCV, 27 (2021) 68 References
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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
  1. 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]
  2. 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]
  3. A. Davini and A. Siconolfi, Metric techniques for convex stationary ergodic Hamiltonians. Calc. Variat. Partial Differ. Equ. 40 (2011) 391–421. [CrossRef] [Google Scholar]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. W. Fleming and H. Soner, Controlled Markov Processes and Viscosity Solutions Stochastic Modelling and Applied Probability, Springer New York (2006). [Google Scholar]
  10. H. Ishii, Almost periodic homogenization of Hamilton-Jacobi equations. Int. Conf. Differ. Equ. 1 (2000). [Google Scholar]
  11. 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]
  12. 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]
  13. U. Krengel and A. Brunel, Ergodic Theorems. De Gruyter Studies in Mathematics, De Gruyter (1985). [Google Scholar]
  14. P.-L. Lions, G. Papanicolaou and S.R. Varadhan, Homogenization of Hamilton-Jacobi equations. unpublished (1986). [Google Scholar]
  15. 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]
  16. 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]
  17. F. Rezakhanlou and J.E. Tarver, Homogenization for stochastic Hamilton-Jacobi equations. Arch. Ratl. Mech. Anal. 151 (2000) 277–309. [Google Scholar]
  18. E. Roxin, The existence of optimal controls. Michigan Math. J. 9 (1962) 109–119. [Google Scholar]
  19. H. Royden, Real Analysis. Mathematics and statistics, Macmillan (1988). [Google Scholar]
  20. P.E. Souganidis, Stochastic homogenization of Hamilton–Jacobi equations and some applications. Asymptotic Anal. 20 (1999) 1–11. [Google Scholar]
  21. A. Stoddart, Existence of optimal controls. Pacific J. Math. 20 (1967) 167–177. [Google Scholar]
  22. B. Ziliotto, Stochastic Homogenization of Nonconvex Hamilton-Jacobi Equations: A Counterexample. Commun. Pure Appl. Math. (2015) arXiv:1512.06375.. [Google Scholar]

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