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Selection of critical solutions in non-monotone vanishing discount problems
Panrui Ni, Jun Yan, Maxime Zavidovique
We study a generalized vanishing discount problem for Hamilton--Jacobi equations without assuming monotonicity either pointwise or in the averaged sense with respect to all Mather…
Sharp convergence rates for the vanishing discount problem with hyperbolic Aubry sets
Panrui Ni
Let be a Tonelli Hamiltonian on a closed connected manifold and let solve \[ λu_λ+H(x,Du_λ)=c(H)\qquad\text{in }M. \] We study the convergence rate of …
A PDE formulation of Lyapunov stability for contact-type Hamilton-Jacobi equations
Panrui Ni, Jun Yan
We study the Lyapunov stability of stationary solutions to contact-type Hamilton-Jacobi equations on a compact manifold. Previous works typically assume Tonelli Hamiltonians…
Static class-guided selection of elementary solutions in non-monotone vanishing discount problems
Panrui Ni, Jun Yan, Maxime Zavidovique
We study a generalized vanishing discount problem for Hamilton--Jacobi equations, removing the standard monotonicity assumption, either in a global sense or when integrated against…