Smooth subsolutions of the discounted Hamilton-Jacobi equations

Liang Jin, Jianlu Zhang, Kai Zhao

Published 2020-07-21Version 1

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