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Optimal semiconcavity with fractional modulus for Hamilton-Jacobi equations with Neumann boundary conditions
Hiroyoshi Mitake, Panrui Ni
We study the semiconcavity property of viscosity solutions to Hamilton--Jacobi equations with Neumann boundary conditions. Unlike the state-constraint case, minimizing trajectories…
Quantitative homogenization of convex Hamilton-Jacobi equations with -periodic Hamiltonians
Hiroyoshi Mitake, Panrui Ni, Hung V. Tran
Here, we study quantitative homogenization of first-order convex Hamilton-Jacobi equations with -periodic Hamiltonians which typically appear in dislocation dynami…
Quantitative homogenization of convex Hamilton-Jacobi equations with Neumann type boundary conditions
Hiroyoshi Mitake, Panrui Ni
We study the periodic homogenization for convex Hamilton-Jacobi equations on perforated domains under the Neumann type boundary conditions. We consider two types of conditions, the…
Rate of convergence for homogenization of nonlinear weakly coupled Hamilton-Jacobi systems
Hiroyoshi Mitake, Panrui Ni
Here, we study the periodic homogenization problem of nonlinear weakly coupled systems of Hamilton-Jacobi equations in the convex setting. We establish a rate of convergence $O(\sq…
Time periodic solutions of first order mean field games from the perspective of Mather theory
Panrui Ni
In this paper, the existence of non-trivial time periodic solutions of first order mean field games is proved. It is assumed that there is a non-trivial periodic orbit contained in…