Calculus of Variations and Geometric Measure Theory

O. Alvarez - M. Bardi - C. Marchi

Multiscale problems and homogenization for second-order Hamilton-Jacobi equations

created by bardi on 21 Nov 2005
modified on 08 Feb 2008


Published Paper

Inserted: 21 nov 2005
Last Updated: 8 feb 2008

Journal: J. Differential Equations
Volume: 243
Pages: 349-387
Year: 2007


We prove a general convergence result for singular perturbations with an arbirtary number of scales of fully nonlinear degenerate parabolic PDEs. As a special case we cover the iterated homogenization for such equations with oscillating initial data. Explicit examples, among others, are the two-scale homogenization of quasilinear equations driven by a general hypoelliptic operator and the $n$-scale homogenization of uniformly parabolic fully nonlinear PDEs.

Keywords: Viscosity solutions, iterated homogenization, hypoelliptic operators, nonlinear parabolic equations