Table of Contents

• Introduction to viscosity solutions for Hamilton-Jacobi equations
• First-order Hamilton-Jacobi equations with convex Hamiltonians
• First-order Hamilton-Jacobi equations with possibly nonconvex Hamiltonians
• Periodic homogenization theory for Hamilton-Jacobi equations
• Almost periodic homogenization theory for Hamilton-Jacobi equations
• First-order convex Hamilton-Jacobi equations in a torus
• Introduction to weak KAM theory
• Further properties of the effective Hamiltonians in the convex setting
• Notations
• Sion's minimax theorem
• Characterization of the Legendre transform
• Existence and regularity of minimizers for action functionals
• Boundary value problems
• Sup-convolutions
• Sketch of proof of Theorem 6.26
• Solutions to some exercises
• Bibliography
• Index