Smooth subsolutions of the discounted Hamilton-Jacobi equations

Abstract

For the discounted Hamilton-Jacobi equation,$$\lambda u+H(x,d_{x}u)=0,x\in M,$$we construct $C^{1,1}$ subsolutions which are indeed solutions on the projected Aubry set. The smoothness of such subsolutions can be improved under additional hyperbolicity assumptions. As applications, we can use such subsolutions to identify the maximal global attractor of the associated conformally symplectic flow and to control the convergent speed of the Lax-Oleinik semigroups

References in corpus (3)

• Convergence of the solutions of the discounted equation
• Convergence of the solutions of the discounted equation: the discrete case
• The rate of convergence of new Lax-Oleinik type operators for time-periodic positive definite Lagrangian systems

Cited by in corpus (2)

• A novel approach to contact Hamiltonians and contact Hamilton-Jacobi theory
• Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities