Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media

154 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Stochastic homogenization of Hamilton-Jacobi and degenerate Bellman equations in unbounded environments (2011, methodology): “We also mention the work of Caffarelli, Souganidis and Wang [4] on the stochastic homogenization of uniformly elliptic equations of second-order, Caffarelli and Souganidis [3] who obtained a rate of convergence for the latter in strongly mixing environments, and Schwab [30] on the homogenization of ”
Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form (2013, background): “Rather than constraining the solutions via the introduction of an obstacle and measuring the extent to which the solutions feel the constraint, as in [5,6], we allow the solutions to be free and measure the curvature of their graphs.”
Asymptotic and numerical homogenization (2008, background): “(5.10) The main result obtained in Caffarelli et al. (2005) is as follows.”
Homogenization of “Viscous” Hamilton–Jacobi Equations in Stationary Ergodic Media (2005, methodology): “The techniques of Caffarelli et al. (2005) rely heavily on the uniform in ellipticity of the equation; hence they cannot be used here.”