@article{AIHPC_2005__22_5_667_0, author = {Lions, Pierre-Louis and Souganidis, Panagiotis E.}, title = {Homogenization of degenerate second-order {PDE} in periodic and almost periodic environments and applications}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {667--677}, publisher = {Elsevier}, volume = {22}, number = {5}, year = {2005}, doi = {10.1016/j.anihpc.2004.10.009}, mrnumber = {2171996}, zbl = {02235973}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.anihpc.2004.10.009/} }
TY - JOUR AU - Lions, Pierre-Louis AU - Souganidis, Panagiotis E. TI - Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications JO - Annales de l'I.H.P. Analyse non linéaire PY - 2005 SP - 667 EP - 677 VL - 22 IS - 5 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2004.10.009/ DO - 10.1016/j.anihpc.2004.10.009 LA - en ID - AIHPC_2005__22_5_667_0 ER -
%0 Journal Article %A Lions, Pierre-Louis %A Souganidis, Panagiotis E. %T Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications %J Annales de l'I.H.P. Analyse non linéaire %D 2005 %P 667-677 %V 22 %N 5 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2004.10.009/ %R 10.1016/j.anihpc.2004.10.009 %G en %F AIHPC_2005__22_5_667_0
Lions, Pierre-Louis; Souganidis, Panagiotis E. Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 5, pp. 667-677. doi : 10.1016/j.anihpc.2004.10.009. https://www.numdam.org/articles/10.1016/j.anihpc.2004.10.009/
[1] Quasi-periodic homogenizations for second-order Hamilton-Jacobi-Bellman equations, Adv. Math. Sci. Appl. 11 (2001) 465-480. | MR | Zbl
,[2] On ergodic stochastic control, Comm. Partial Differential Equations 23 (1998) 2187-2217. | MR | Zbl
, ,[3] A weak Bernstein method for fully nonlinear elliptic equations, Differential Integral Equations 4 (1991) 241-262. | MR | Zbl
,[4] Controlled diffusions in a random medium, Stochastics 24 (1988) 87-120. | MR | Zbl
, ,[5] Homogenization of a Hamilton-Jacobi equation associated with the geometric motion of an interface, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 773-805. | MR | Zbl
, ,[6] Approximations of effective coefficients in stochastic homogenization, Ann. Inst. H. Poincaré Probab. Statist. 40 (2004) 153-165. | Numdam | MR | Zbl
, ,[7] Fully nonlinear elliptic partial differential equations, Amer. Math. Soc., 1997.
, ,[8] A note on nonlinear homogenization, Comm. Pure Appl. Math. 52 (1999) 829-838. | MR | Zbl
,[9] L.A. Caffarelli, P.-L., Lions, P.E. Souganidis, in preparation.
[10] Stochastic homogenization for fully nonlinear, second-order partial differential equations, Comm. Pure Appl. Math. LVII (2005) 319-361. | MR | Zbl
, , ,[11] Homogenization of random semilinear PDEs, Probab. Theory Related Fields 121 (2001) 492-524. | MR | Zbl
,[12] Periodic homogenization of Hamilton-Jacobi equations: additive eigenvalue and variational formulas, Indiana Univ. Math. J. 45 (1996) 1095-1117. | MR | Zbl
,[13] User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27 (1992) 1-67. | MR | Zbl
, , ,[14] Nonlinear stochastic homogenization and ergodic theory, J. Reine Angew. Math. 368 (1986) 28-42. | MR | Zbl
, ,[15] N. Dirr, A. Yip, personal communication.
[16] A class of homogenization problems in the calculus of variations, Comm. Pure Appl. Math. XLIV (1991) 733-759. | MR | Zbl
,[17] Periodic homogenization of certain fully nonlinear partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992) 245-265. | MR | Zbl
,[18] The perturbed test function method for viscosity solutions of nonlinear pde, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989) 359-375. | MR | Zbl
,[19] On factorization of a non-negative definite matrix, Probab. Theory Appl. 13 (1968) 375-378, (in Russian). | Zbl
,[20] Almost periodic homogenization of Hamilton-Jacobi equations, in: Int. Conf. on Diff. Eqs., vol. 1, Berlin 1999, World Scientific, River Edge, NJ, 2000, pp. 600-605. | MR | Zbl
,[21] Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, JDE 83 (1990) 26-78. | MR | Zbl
, ,[22] Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, 1991. | MR | Zbl
, , ,[23] H. Kosynga, F. Rezankhanlou, S.R.S. Varadhan, Stochastic homogenization of Hamilton-Jacobi-Bellman equations, Preprint.
[24] The method of averaging and walks in inhomogeneous environments, Russian Math. Surveys 40 (1985) 73-145. | MR | Zbl
,[25] Resolution de problemes elliptic quasilineaires, Arch. Rational Mech. Anal. 74 (1980) 335-353. | MR | Zbl
,[26] Correctors for the homogenization of Hamilton-Jacobi equations in a stationary ergodic setting, Comm. Pure Appl. Math. LVI (2003) 1501-1524. | MR | Zbl
, ,[27] Homogenization of “viscous” Hamilton-Jacobi equations in stationary ergodic media, Comm. Partial Differential Equations 30 (2005) 335-375. | Zbl
, ,[28] P.-L. Lions, P.E. Souganidis, in preparation.
[29] P.-L. Lions, G. Papanicolaou, S.R.S. Varadhan, Homogenization of Hamilton-Jacobi equations, Preprint.
[30] Large scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales, Nonlinearity 7 (1994) 1-30. | MR | Zbl
, ,[31] S. Müller, private communication.
[32] Alcuni visultati sulle equazioni lineari e quasilineri ellitico-paraboliche a derivate parziali del second ordine, Rend. Classe Sci. Fis. Mat., Nat. Acad. Naz. Lincei, Sci. 8 40 (1966) 774-784. | Zbl
,[33] Boundary value problems with rapidly oscillating random coefficients, in: , , (Eds.), Rigorous Results in Statistical Mechanics and Quantum Field Theory, Proc. Colloq. on Random Fields, Colloquia Mathematica Societ. Janos Bolyai, vol. 10, 1979, pp. 835-873. | MR | Zbl
, ,[34] Diffusion with random coefficients, in: (Ed.), Essays in Statistics and Probability, North-Holland, 1981. | MR | Zbl
, ,[35] Homogenization for stochastic Hamilton-Jacobi equations, Arch. Rational Mech. Anal. 151 (2000) 277-309. | MR | Zbl
, ,[36] The problem of Dirichlet of quasilinear elliptic differential equations with many independent variables, Philos. Trans. Roy. Soc. London Ser. A 264 (1969) 413-469. | MR | Zbl
,[37] Front propagation: Theory and applications, in: CIME Course on “Viscosity Solutions and their Applications”, Lecture Notes in Math., vol. 1660, Springer, 1997. | Zbl
,[38] Recent developments in the theory of front propagation and its applications, in: (Ed.), Modern Methods in Scientific Computing and Applications, NATO Science Ser. II, vol. 75, Kluwer Academic, 2002. | MR | Zbl
,[39] Stochastic homogenization of Hamilton-Jacobi equations and some applications, Asymptotic Anal. 20 (1999) 1-11. | MR | Zbl
,- Stochastic homogenization of quasiconvex degenerate viscous HJ equations in 1d, Calculus of Variations and Partial Differential Equations, Volume 64 (2025) no. 2 | DOI:10.1007/s00526-024-02870-x
- Bifurcation of homogenization and nonhomogenization of the curvature G-equation with shear flows, Mathematische Annalen, Volume 391 (2025) no. 2, p. 3077 | DOI:10.1007/s00208-024-02983-w
- Periodic homogenization of geometric equations without perturbed correctors, Mathematische Annalen, Volume 391 (2025) no. 2, p. 3143 | DOI:10.1007/s00208-024-02998-3
- Lagrangian, game theoretic, and PDE methods for averaging G-equations in turbulent combustion: existence and beyond, Bulletin of the American Mathematical Society, Volume 61 (2024) no. 3, p. 470 | DOI:10.1090/bull/1838
- The generalized anisotropic dynamical Wentzell heat equation with nonstandard growth conditions, Journal d'Analyse Mathématique, Volume 152 (2024) no. 2, p. 615 | DOI:10.1007/s11854-023-0306-z
- A convergence rate of periodic homogenization for forced mean curvature flow of graphs in the laminar setting, Nonlinear Differential Equations and Applications NoDEA, Volume 31 (2024) no. 3 | DOI:10.1007/s00030-024-00929-4
- Existence of an Effective Burning Velocity in a Cellular Flow for the Curvature G-Equation Proved Using a Game Analysis, The Journal of Geometric Analysis, Volume 34 (2024) no. 3 | DOI:10.1007/s12220-023-01523-3
- Homogenization of the Allen–Cahn equation with periodic mobility, Calculus of Variations and Partial Differential Equations, Volume 61 (2022) no. 3 | DOI:10.1007/s00526-022-02199-3
- Level-set forced mean curvature flow with the Neumann boundary condition, Journal de Mathématiques Pures et Appliquées, Volume 168 (2022), p. 143 | DOI:10.1016/j.matpur.2022.11.002
- Optimal Control of Diffusion Processes with Terminal Constraint in Law, Journal of Optimization Theory and Applications, Volume 195 (2022) no. 1, p. 1 | DOI:10.1007/s10957-022-02053-8
- Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations, Memoirs of the American Mathematical Society, Volume 280 (2022) no. 1381 | DOI:10.1090/memo/1381
- Steiner symmetrization for anisotropic quasilinear equations via partial discretization, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 38 (2021) no. 2, p. 347 | DOI:10.1016/j.anihpc.2020.07.005
- Convergence rates in almost-periodic homogenization of higher-order elliptic systems, Asymptotic Analysis, Volume 123 (2021) no. 1-2, p. 95 | DOI:10.3233/asy-201627
- Stochastic homogenization of a class of quasiconvex viscous Hamilton-Jacobi equations in one space dimension, Journal of Differential Equations, Volume 300 (2021), p. 660 | DOI:10.1016/j.jde.2021.08.004
- Head and Tail Speeds of Mean Curvature Flow with Forcing, Archive for Rational Mechanics and Analysis, Volume 235 (2020) no. 1, p. 287 | DOI:10.1007/s00205-019-01423-3
- Spreading speeds of KPP-type lattice systems in heterogeneous media, Communications in Contemporary Mathematics, Volume 22 (2020) no. 01, p. 1850083 | DOI:10.1142/s0219199718500839
- Weak KAM theory for potential MFG, Journal of Differential Equations, Volume 268 (2020) no. 7, p. 3255 | DOI:10.1016/j.jde.2019.09.060
- Spreading speeds of nonlocal KPP equations in almost periodic media, Journal of Functional Analysis, Volume 279 (2020) no. 9, p. 108723 | DOI:10.1016/j.jfa.2020.108723
- Multiple Scale Homogenisation of Nutrient Movement and Crop Growth in Partially Saturated Soil, Bulletin of Mathematical Biology, Volume 81 (2019) no. 10, p. 3778 | DOI:10.1007/s11538-019-00656-3
- Some new results on Lipschitz regularization for parabolic equations, Journal of Evolution Equations, Volume 19 (2019) no. 4, p. 1149 | DOI:10.1007/s00028-019-00512-w
- Curvature Effect in Shear Flow: Slowdown of Turbulent Flame Speeds with Markstein Number, Communications in Mathematical Physics, Volume 359 (2018) no. 2, p. 515 | DOI:10.1007/s00220-017-3060-1
- Viscosity methods for large deviations estimates of multiscale stochastic processes, ESAIM: Control, Optimisation and Calculus of Variations, Volume 24 (2018) no. 2, p. 605 | DOI:10.1051/cocv/2017051
- Approximate correctors and convergence rates in almost-periodic homogenization, Journal de Mathématiques Pures et Appliquées, Volume 110 (2018), p. 187 | DOI:10.1016/j.matpur.2017.09.014
- Asymptotics for Small Nonlinear Price Impact: A PDE Homogenization Approach to the Multidimensional Case, SSRN Electronic Journal (2018) | DOI:10.2139/ssrn.3287099
- Generalized Transition Fronts for One-Dimensional Almost Periodic Fisher-KPP Equations, Archive for Rational Mechanics and Analysis, Volume 223 (2017) no. 3, p. 1239 | DOI:10.1007/s00205-016-1056-1
- Homogenization of a semilinear heat equation, Journal de l’École polytechnique — Mathématiques, Volume 4 (2017), p. 633 | DOI:10.5802/jep.54
- Lipschitz regularity results for nonlinear strictly elliptic equations and applications, Journal of Differential Equations, Volume 263 (2017) no. 7, p. 4324 | DOI:10.1016/j.jde.2017.05.020
- Higher Order Convergence Rates in Theory of Homogenization: Equations of Non-divergence Form, Archive for Rational Mechanics and Analysis, Volume 219 (2016) no. 3, p. 1273 | DOI:10.1007/s00205-015-0921-7
- On the first eigenpair of singularly perturbed operators with oscillating coefficients, Communications in Partial Differential Equations, Volume 41 (2016) no. 1, p. 1 | DOI:10.1080/03605302.2015.1091838
- Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems, Nonlinear Analysis, Volume 130 (2016), p. 76 | DOI:10.1016/j.na.2015.09.012
- Nonlinear elliptic systems and mean-field games, Nonlinear Differential Equations and Applications NoDEA, Volume 23 (2016) no. 4 | DOI:10.1007/s00030-016-0397-7
- Convergence rates and Hölder estimates in almost-periodic homogenization of elliptic systems, Analysis PDE, Volume 8 (2015) no. 7, p. 1565 | DOI:10.2140/apde.2015.8.1565
- Homogenization and Asymptotics for Small Transaction Costs: The Multidimensional Case, Communications in Partial Differential Equations, Volume 40 (2015) no. 11, p. 2005 | DOI:10.1080/03605302.2015.1053916
- A priori gradient bounds for fully nonlinear parabolic equations and applications to porous medium models, Journal de Mathématiques Pures et Appliquées, Volume 103 (2015) no. 6, p. 1346 | DOI:10.1016/j.matpur.2014.11.001
- Counter-Example in Three Dimension and Homogenization of Geometric Motions in Two Dimension, Archive for Rational Mechanics and Analysis, Volume 212 (2014) no. 2, p. 503 | DOI:10.1007/s00205-013-0712-y
- Large Deviations and Importance Sampling for Systems of Slow-Fast Motion, Applied Mathematics Optimization, Volume 67 (2013) no. 1, p. 123 | DOI:10.1007/s00245-012-9183-z
- The homogenization of surfaces and boundaries, Bulletin of the Brazilian Mathematical Society, New Series, Volume 44 (2013) no. 4, p. 755 | DOI:10.1007/s00574-013-0033-7
- Long-Time Behavior of the Mean Curvature Flow with Periodic Forcing, Communications in Partial Differential Equations, Volume 38 (2013) no. 5, p. 780 | DOI:10.1080/03605302.2013.771508
- Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem, ESAIM: Control, Optimisation and Calculus of Variations, Volume 18 (2012) no. 4, p. 954 | DOI:10.1051/cocv/2011203
- Spreading speeds for one-dimensional monostable reaction-diffusion equations, Journal of Mathematical Physics, Volume 53 (2012) no. 11 | DOI:10.1063/1.4764932
- Importance Sampling for Multiscale Diffusions, Multiscale Modeling Simulation, Volume 10 (2012) no. 1, p. 1 | DOI:10.1137/110842545
- A Quantitative Description of Mesh Dependence for the Discretization of Singularly Perturbed Nonconvex Problems, SIAM Journal on Numerical Analysis, Volume 50 (2012) no. 4, p. 1883 | DOI:10.1137/110822001
- Periodic traveling waves of a mean curvature equation in high dimensional cylinders, Applied Mathematics and Computation, Volume 217 (2011) no. 22, p. 9267 | DOI:10.1016/j.amc.2011.04.004
- Homogenization limit of a parabolic equation with nonlinear boundary conditions, Journal of Differential Equations, Volume 251 (2011) no. 6, p. 1447 | DOI:10.1016/j.jde.2011.06.002
- On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems, Networks Heterogeneous Media, Volume 6 (2011) no. 1, p. 61 | DOI:10.3934/nhm.2011.6.61
- Homogenization of Fronts in Highly Heterogeneous Media, SIAM Journal on Mathematical Analysis, Volume 43 (2011) no. 1, p. 212 | DOI:10.1137/100800014
- Motion and Pinning of Discrete Interfaces, Archive for Rational Mechanics and Analysis, Volume 195 (2010) no. 2, p. 469 | DOI:10.1007/s00205-009-0215-z
- Rates of convergence for the homogenization of fully nonlinear uniformly elliptic pde in random media, Inventiones mathematicae, Volume 180 (2010) no. 2, p. 301 | DOI:10.1007/s00222-009-0230-6
- Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients, Networks Heterogeneous Media, Volume 5 (2010) no. 4, p. 745 | DOI:10.3934/nhm.2010.5.745
- Hölder estimates for degenerate elliptic equations with coercive Hamiltonians, Transactions of the American Mathematical Society, Volume 362 (2010) no. 9, p. 4511 | DOI:10.1090/s0002-9947-10-04807-5
- Hölder and Lipschitz Estimates for Viscosity Solutions of Some Degenerate Elliptic PDE’s, Analysis, Partial Differential Equations and Applications (2009), p. 31 | DOI:10.1007/978-3-7643-9898-9_4
- A discussion about the homogenization of moving interfaces, Journal de Mathématiques Pures et Appliquées, Volume 91 (2009) no. 4, p. 339 | DOI:10.1016/j.matpur.2009.01.014
- Rates of convergence in periodic homogenization of fully nonlinear uniformly elliptic PDEs, Nonlinearity, Volume 22 (2009) no. 6, p. 1481 | DOI:10.1088/0951-7715/22/6/011
- Asymptotic and numerical homogenization, Acta Numerica, Volume 17 (2008), p. 147 | DOI:10.1017/s0962492906360011
- Homogenization of Hamilton‐Jacobi‐Bellman equations with respect to time‐space shifts in a stationary ergodic medium, Communications on Pure and Applied Mathematics, Volume 61 (2008) no. 6, p. 816 | DOI:10.1002/cpa.20220
- Pulsating wave for mean curvature flow in inhomogeneous medium, European Journal of Applied Mathematics, Volume 19 (2008) no. 6, p. 661 | DOI:10.1017/s095679250800764x
- Multiscale problems and homogenization for second-order Hamilton–Jacobi equations, Journal of Differential Equations, Volume 243 (2007) no. 2, p. 349 | DOI:10.1016/j.jde.2007.05.027
- Hölder estimates for viscous Hamilton–Jacobi equations, PAMM, Volume 7 (2007) no. 1, p. 1040201 | DOI:10.1002/pamm.200700239
Cité par 58 documents. Sources : Crossref