48 citations · 201 across the 25 of their papers we have counts for
6 papers · 1 filter
Averaging of Hamilton-Jacobi equations over Hamiltonian flows
Hitoshi Ishii, Taiga Kumagai
We study the asymptotic behavior of solutions to the Dirichlet problem for Hamilton-Jacobi equations with large drift terms, where the drift terms are given by the Hamiltonian vect…
Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii
We investigate positivity sets of nonnegative supersolutions of the fully nonlinear elliptic equations in , where is an open subset of , an…
The Vanishing Discount problem for Hamilton-Jacobi Equations in the Euclidean Space
Hitoshi Ishii, Antonio Siconolfi
We study the asymptotic behavior of the solutions to a family of discounted Hamilton Jacobi equations, posed in the Euclidean N dimensional space, when the discount factor goes to…
The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 2: Nonlinear coupling
Hitoshi Ishii, Liang Jin
We study the vanishing discount problem for a nonlinear monotone system of Hamilton-Jacobi equations. This continues the first author's investigation on the vanishing discount prob…
The vanishing discount problem for monotone systems of Hamilton-Jacobi equations. Part 1: linear coupling
Hitoshi Ishii
We establish a convergence theorem for the vanishing discount problem for a weakly coupled system of Hamilton-Jacobi equations. The crucial step is the introduction of Mather measu…
Existence through convexity for the truncated Laplacians
Isabeau Birindelli, Giulio Galise, Hitoshi Ishii
We study the Dirichlet problem on a bounded convex domain of , with zero boundary data, for truncated Laplacians , with . We establish a neces…