This book gives an extensive survey of many important topics in the theory of Hamilton–
Jacobi equations with particular emphasis on modern approaches and viewpoints. Firstly …

Fast Marching and Fast Sweeping are the two most commonly used methods for solving the
eikonal equation. Each of these methods performs best on a different set of problems. Fast …

We study the discretization of the escape time problem: find the length of the shortest path
joining an arbitrary point zz of a domain Ω Ω, to the boundary ∂ Ω∂ Ω. Path length is …

We present a simple, new proof for the stochastic homogenization of quasiconvex (level-set
convex) Hamilton–Jacobi equations set in stationary ergodic environments. Our approach …

We present exponential error estimates and demonstrate an algebraic convergence rate for
the homogenization of level-set convex Hamilton-Jacobi equations in iid random …

We present a proof of qualitative stochastic homogenization for a nonconvex Hamilton–
Jacobi equations. The new idea is to introduce a family of “sub-equations” and to control …

In the first part of the paper, we propose and rigorously analyze a mixed finite element
method for the approximation of the periodic strong solution to the fully nonlinear second …

Numerous applications of Eikonal equations prompted the development of many efficient
numerical algorithms. The Heap-Cell Method (HCM) is a recent serial two-scale technique …

This paper is the first attempt to systematically study properties of the effective Hamiltonian
HH¯ arising in the periodic homogenization of some coercive but nonconvex Hamilton …

We propose a new formulation to compute effective Hamiltonians for homogenization of a
class of Hamilton–Jacobi equations. Our formulation utilizes an observation made by Barron …