6 citations · 18 across the 16 of their papers we have counts for
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On the inhomogeneous discounted Hamilton-Jacobi equations
Liang Jin, Jun Yan, Kai Zhao
In this paper, we study the family of inhomogeneous discounted Hamilton-Jacobi equations \begin{equation}\label{hjs1} λ(x)u+h(x,d_x u)=c \quad \tag{} \end{equation} on a clos…
Nonlinear semigroup approach to Hamilton-Jacobi equations -- A toy model
Liang Jin, Jun Yan, Kai Zhao
In this paper, we discuss the existence and multiplicity problem of viscosity solution to the Hamilton-Jacobi equation where is a closed ma…
Herglotz' variational principle and Lax-Oleinik evolution
Piermarco Cannarsa, Wei Cheng, Liang Jin +2
We develop an elementary method to give a Lipschitz estimate for the minimizers in the problem of Herglotz' variational principle proposed in \cite{CCWY2018} in the time-dependent…
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…
A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect
Liang Jin, Lin Wang, Jun Yan
Based on a fixed point argument, we give a {\it dynamical representation} of the viscosity solution to Cauchy problem of certain weakly coupled systems of Hamilton-Jacobi equations…