The paper reviews GHGF for HJ equations and proves a minimizing-movement construction for generalized characteristics plus that GHGF semi-flow invariant measures attaining c[H] are exactly the projected Mather measures.
Generic properties and problems of minimizing measures of La- grangian systems.Nonlinearity, 9(2):273–310, 1996
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Recent progress in generalized Hamiltonian gradient flow: Singularities
The paper reviews GHGF for HJ equations and proves a minimizing-movement construction for generalized characteristics plus that GHGF semi-flow invariant measures attaining c[H] are exactly the projected Mather measures.