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math.AP2024
Long-time behavior of generalized gradient flows of solutions to Hamilton-Jacobi equations
Paolo Albano, Piermarco Cannarsa, Wei Cheng +1
We study the long-time behavior of the generalized gradient flow associated with solutions of the critical Hamilton-Jacobi equation for mechanical Hamiltonians on the flat torus. F…
math.AP2024
Variational construction of singular characteristics and propagation of singularities
Piermarco Cannarsa, Wei Cheng, Jiahui Hong +1
On a smooth closed manifold , we introduce a novel theory of maximal slope curves for any pair with a semiconcave function and a Hamiltonian. By using the notion…
math.AP2024
Optimal transport in the frame of abstract Lax-Oleinik operator revisited
Wei Cheng, Jiahui Hong, Tianqi Shi
This is our first paper on the extension of our recent work on the Lax-Oleinik commutators and its applications to the intrinsic approach of propagation of singularities of the vis…