JournalsaihpcVol. 22, No. 5pp. 667–677

Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications

  • Pierre-Louis Lions

    College de France, 11, place Marcelin Berthelot, Paris 75005, France, CEREMADE, Université de Paris-Dauphine, place du Marechal de Lattre de Tassigny, Paris Cedex 16, France

  • Panagiotis E. Souganidis

    Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, TX 78712-0257, USA
Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications cover
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Abstract

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.

Cite this article

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. 667–677

DOI 10.1016/J.ANIHPC.2004.10.009