6 papers · 1 filter
Vanishing discount and viscosity selection problems for mechanical Hamilton--Jacobi equations
Hiroyoshi Mitake, Panrui Ni, Hung V. Tran
We study simultaneous vanishing discount and viscosity limits for mechanical Hamilton--Jacobi equations on the -dimensional torus. In the critical regime, we explicitly identify…
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…
On equivalence of entropy and viscosity solutions to degenerate parabolic equations and applications
Hiroyoshi Mitake, Hiroshi Watanabe
Here, we consider anisotropic degenerate parabolic-hyperbolic equations and degenerate quasilinear Hamilton-Jacobi equations. We prove the equivalence of two notions of entropy and…