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Abstract |
We introduce a notion of upper Green regular solutions to Tonelli Hamilton-Jacobi equations. Then we prove some weak $C^2$ convergence results to such a solution for a large class of approximated solutions as the discounted solution, the image of a $C^0$ function by the Lax-Oleinik semi-group, the weak KAM solutions for perturbed cohomology class. Moreover, we provide several examples or counter-examples, especially the one that is not upper Green regular and to which we have $C^1$ convergence but not convergence in measure of the second derivatives. This is a joint work with Marie-Claude Arnaud. |
