Differentiability of Mather's beta function in low dimensions

Abstract

Let L be a time-periodic Lagrangian on a two-torus. Then the beta-function of L is differentiable at least in k directions at any k-irrational homology class, for k= 0, 1, 2.

New version which focuses on the two-torus case

References in corpus (2)

• Subsolutions of time-periodic Hamilton-Jacobi equations
• Aubry sets vs Mather sets in two degrees of freedom