 
Summary: PHYSICAL SOLUTIONS OF THE HAMILTONJACOBI
EQUATION
NALINI ANANTHARAMAN, RENATO ITURRIAGA, PABLO PADILLA,
AND H´ECTOR S´ANCHEZMORGADO
Abstract. We consider a Lagrangian system on the ddimensional
torus, and the associated HamiltonJacobi equation. Assuming
that the Aubry set of the system consists in a finite number of hy
perbolic periodic orbits of the EulerLagrange flow, we study the
vanishingviscosity limit, from the viscous equation to the inviscid
problem. Under suitable assumptions, we show that solutions of
the viscous HamiltonJacobi equation converge to a unique solution
of the inviscid problem.
1. Introduction
Let L be a strictly convex and superlinear Lagrangian of class C3
on
the ddimensional torus Td
, and let H be the associated Hamiltonian
via the Legendre transformation:
L : Td
× Rd
