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Homogenization and Non-Homogenization of certain Non-Convex Hamilton-Jacobi Equations by Feldman, William M.; Souganidis, Panagiotis E. is a scholarly article available to read on EtoBox.

What is Homogenization and Non-Homogenization of certain Non-Convex Hamilton-Jacobi Equations about?

We continue the study of the homogenization of coercive non-convex Hamilton-Jacobi equations in random media identifying two general classes of Hamiltonians with very distinct behavior. For the first class there is no homogenization in a particular environment while for the second homogenization takes place in environments with finite range dependence. Motivated by the recent counter-example of Ziliotto, who constructed a coercive but non-convex Hamilton-Jacobi equation with stationary ergodic random potential field for which homogenization does not hold, we show that same happens for coercive Hamiltonians which have a strict saddle-point, a very local property. We also identify, based on the recent work of Armstrong and Cardaliaguet on the homogenization of positively homogeneous random Hamiltonians in environments with finite range dependence, a new general class Hamiltonians, namely equations with uniformly strictly star-shaped sub-level sets, which homogenize.

Author

Feldman, William M.; Souganidis, Panagiotis E.

Published

2016

Language

EN