Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 43
Number of page(s) 22
DOI https://doi.org/10.1051/cocv/2023038
Published online 09 June 2023
  1. Y. Achdou and S. Patrizi, Homogenization of first-order equations with u/ϵ-periodic Hamiltonian: rate of convergence as ϵ → 0 and numerical methods. Math. Models Methods Appl. Sci. 21 (2011) 1317–1353. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Arisawa, Homogenizations of integro-differential equations with Lévy operators with asymmetric and degenerate densities. Proc. Roy. Soc. Edinb. Sect. A 142 (2012) 917–943. [CrossRef] [Google Scholar]
  3. M. Bardi, A. Cesaroni and E. Topp, Cauchy problem and periodic homogenization for nonlocal Hamilton–Jacobi equations with coercive gradient terms. Proc. Roy. Soc. Edinb. Sect. A 150 (2020) 3028–3059. [CrossRef] [Google Scholar]
  4. M. Bardi and G. Terrone, Periodic homogenization of deterministic control problems via limit occupational measures, in Dynamics, Games and Science, Vol. 1 of CIM Ser. Math. Sci. Springer, Cham (2015) 105–116. [CrossRef] [Google Scholar]
  5. G. Barles, E. Chasseigne, A. Ciomaga and C. Imbert, Lipschitz regularity of solutions for mixed integro-differential equations. J. Diff. Equ. 252 (2012) 6012–6060. [CrossRef] [Google Scholar]
  6. G. Barles, E. Chasseigne, A. Ciomaga and C. Imbert, Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations. Calc. Var. Partial Diff. Equ. 50 (2022) 283–304. [Google Scholar]
  7. G. Barles and C. Imbert, Second-order elliptic integro-differential equations: viscosity solutions’ theory revisited, Ann. Institut Henri Poincare (C) Non Linear Anal. 25 (2208) 567–585. [Google Scholar]
  8. G. Barles, O. Ley and E. Topp, Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behavior. Nonlinearity 30 (2017) 703–734. [CrossRef] [MathSciNet] [Google Scholar]
  9. L. Caffarelli and L. Silvestre, Regularity theory for fully nonlinear integro-differential equations. Commun.Pure Appl. Math. 62 (2009) 597–638. [CrossRef] [Google Scholar]
  10. F. Camilli and C. Marchi, Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs. Nonlinearity 22 (2009) 1481–1498. [CrossRef] [MathSciNet] [Google Scholar]
  11. I Capuzzo-Dolcetta and H Ishii, On the rate of convergence in homogenization of Hamilton-Jacobi equations. Indiana Univ. Math. J. 50 (2001) 1113–1129. [CrossRef] [Google Scholar]
  12. H. Chang-Lara and G. Davila, Holder estimates for non-local parabolic equations with critical drift. J. Diff. Equ. 260 (2016) 4237–4284. [CrossRef] [Google Scholar]
  13. A. Ciomaga, D. Ghilli and E. Topp, Periodic homogenization for weakly elliptic Hamilton–Jacobi–Bellman equations with critical fractional diffusion. Commun. Partial Diff. Equ. 47 (2022) 1–38. [CrossRef] [Google Scholar]
  14. R. Cont and P. Tankov, Financial Modelling with Jump Processes. Chapman & Hall/CRC (2003). [Google Scholar]
  15. Ph. Courrege, Sur la forme intégro-différentielle des opérateurs de ck dans c satisfaisant au principe du maximum. Sémin. Brelot-Choquet-Deny. Théorie Potentiel. 10 (1965) 1–38. [Google Scholar]
  16. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [Google Scholar]
  17. L.C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE. Proc. Roy. Soc. Edinb. Sect. A: Math. 111 (1989) 359–375. [CrossRef] [Google Scholar]
  18. L.C. Evans, Periodic homogenisation of certain fully nonlinear partial differential equations. Proc. Roy. Soc. Edinb. Sect. A: Math. 120 (1992) 245–265. [CrossRef] [Google Scholar]
  19. N. Guillen, C. Mou and A. Świȩch, Coupling Lévy measures and comparison principles for viscosity solutions. Trans. Amer. Math. Soc. 372 (2019) 7327–7370. [CrossRef] [MathSciNet] [Google Scholar]
  20. N. Guillen and R.W. Schwab, Min–max formulas for nonlocal elliptic operators. Calc. Var. Partial Diff. Equ. 58 (2019) 1–79. [CrossRef] [Google Scholar]
  21. H. Ishii, H. Mitake and H.V. Tran, The vanishing discount problem and viscosity Mather measures. Part 1: The problem on a torus. J. Math. Pures Appl. 108 (2017) 125–149. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Kassmann, A. Piatnitski and E. Zhizhina, Homogenization of Lévy-type operators with oscillating coefficients. SIAM J. Math. Anal. 51 3641–3665. [Google Scholar]
  23. S. Kim and K.-A. Lee, Higher order convergence rates in theory of homogenization: equations of non-divergence form. Arch. Rational Mech. Anal. 219 (2016) 1273–1304. [CrossRef] [MathSciNet] [Google Scholar]
  24. B. Øksendal and A. Sulem, Applied Stochastic Control of Jump Diffusions. Universitext. Springer, Cham (2019). [CrossRef] [Google Scholar]
  25. H. Mitake, H.V. Tran and Y. Yu, Rate of convergence in periodic homogenization of Hamilton-–Jacobi equations: the convex setting. Arch. Rational Mech. Anal. 233 (2019) 901–934. [CrossRef] [MathSciNet] [Google Scholar]
  26. C. Mou and A. Świech, Uniqueness of viscosity solutions for a class of integro-differential equations. Nonlinear Diff. Equ. Applic. NoDEA. 22 1851–1882. [Google Scholar]
  27. G. Papanicolaou, P.L. Lions and S.R.S. Varadhan, Homogeneization of Hamilton–Jacobi equations. Unpublished, 1986. [Google Scholar]
  28. H. Pham, Optimal stopping of controlled jump diffusion processes: a viscosity solution approach. J. Math. Syst. Estim. Control 8 (1998) 1–27. [Google Scholar]
  29. A. Piatnitski and E. Zhizhina, Periodic homogenization of nonlocal operators with a convolution-type kernel. SIAM J. Math. Anal. 49 (2017) 64–81. [CrossRef] [MathSciNet] [Google Scholar]
  30. R.W. Schwab, Periodic homogenization for nonlinear integro-differential equations. SIAM J. Math. Anal. 42 (2010) 2652–2680. [CrossRef] [MathSciNet] [Google Scholar]
  31. J. Serra, Cσ+α regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels. Calc. Var. Partial Diff. Equ. 54 (2015) 3571–3601. [CrossRef] [Google Scholar]
  32. M. Sion, On general minimax theorems. Pacific J. Math. 8 (1958) 171–176. [CrossRef] [MathSciNet] [Google Scholar]
  33. T. Tabet Tchamba, Large time behavior of solutions of viscous Hamilton-Jacobi equations with superquadratic Hamiltonian. Asymptotic Anal. 66 (2010) 161–186. [CrossRef] [MathSciNet] [Google Scholar]
  34. G. Terrone, Limiting relaxed controls and averaging of singularly perturbed deterministic control systems. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 18 (2011) 653–672. [MathSciNet] [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.