We study the homogenization of fully nonlinear degenerate second-order pde, with “ellipticity” of the same order as the space oscillations, in periodic and almost periodic. As a special case we consider the class of quasi-linear, degenerate elliptic pde. The results apply to level sets equations describing the evolution of fronts with prescribed normal velocity. We also discuss an application about the averaged properties of interfacial motions in periodic and almost periodic environments.
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Pierre-Louis Lions, Panagiotis E. Souganidis, Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 5, pp. 667–677DOI 10.1016/J.ANIHPC.2004.10.009