113 citations · 281 across the 17 of their papers we have counts for
20 papers
Stochastic homogenization of quasiconvex degenerate viscous HJ equations in 1d
Andrea Davini
We prove homogenization for degenerate viscous Hamilton-Jacobi equations in dimension one in stationary ergodic environments with a quasiconvex and superlinear Hamiltonian of fairl…
Stochastic homogenization of a class of quasiconvex and possibly degenerate viscous HJ equations in 1d
Andrea Davini
We prove homogenization for possibly degenerate viscous Hamilton-Jacobi equations with a Hamiltonian of the form , where is a quasiconvex, locally Lipschitz functi…
Stochastic homogenization of nondegenerate viscous HJ equations in 1d
Andrea Davini
We prove homogenization for a nondegenerate viscous Hamilton-Jacobi equation in dimension one in stationary ergodic environments with a superlinear (nonconvex) Hamiltonian of fairl…
Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations in one space dimension
Andrea Davini, Elena Kosygina, Atilla Yilmaz
We prove homogenization for viscous Hamilton-Jacobi equations with a Hamiltonian of the form for a wide class of stationary ergodic random media in one space dimensio…
On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case
Italo Capuzzo Dolcetta, Andrea Davini
We study the asymptotic behavior of the viscosity solutions of the Hamilton-Jacobi (HJ) equation \begin{equation*} λu(x)+G(x,u')=c(G)\qquad\hbox{in } \end{equat…
On the vanishing discount problem from the negative direction
Andrea Davini, Lin Wang
It has been proved in [10] that the unique viscosity solution of \begin{equation}\label{abs}\tag{*} λu_λ+H(x,d_x u_λ)=c(H)\qquad\hbox{in }, \end{equation} uniformly converges, f…
Discrete approximation of the viscous HJ equation
Andrea Davini, Hitoshi Ishii, Renato Iturriaga +1
We consider a stochastic discretization of the stationary viscous Hamilton Jacobi equation on the flat d dimensional torus, associated with a Hamiltonian, convex and superlinear in…
Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension
Andrea Davini, Elena Kosygina
We prove homogenization for a class of nonconvex (possibly degenerate) viscous Hamilton-Jacobi equations in stationary ergodic random environments in one space dimension. The resul…
Convergence of the solutions of discounted Hamilton--Jacobi systems
Andrea Davini, Maxime Zavidovique
We consider a weakly coupled system of discounted Hamilton--Jacobi equations set on a closed Riemannian manifold. We prove that the corresponding solutions converge to a specific s…
Homogenization of viscous and non-viscous HJ equations: a remark and an application
Andrea Davini, Elena Kosygina
It was pointed out in [P.L. Lions, G. Papanicolaou, S. Varadhan, Homogenization of Hamilton-Jacobi equation, unpublished preprint (1987)] that, for first order Hamilton-Jacobi (HJ)…
Random Lax--Oleinik semigroups for Hamilton--Jacobi systems
Andrea Davini, Antonio Siconolfi, Maxime Zavidovique
Following the random approach of Mitake, Siconolfi,Tran and Yamada, we define a Lax--Oleinik formula adapted to evolutive weakly coupled systems of Hamilton--Jacobi equations. It i…
Existence and uniqueness of solutions to parabolic equations with superlinear Hamiltonians
Andrea Davini
We give a proof of existence and uniqueness of viscosity solutions to parabolic quasilinear equations for a fairly general class of nonconvex Hamiltonians with superlinear growth i…
Convergence of the solutions of the discounted equation: the discrete case
Andrea Davini, Albert Fathi, Renato Iturriaga +1
We derive a discrete version of the results of our previous work. If is a compact metric space, a continuous cost function and , the u…
Convergence of the solutions of the discounted equation
Andrea Davini, Albert Fathi, Renato Iturriaga +1
We consider a continuous coercive Hamiltonian on the cotangent bundle of the compact connected manifold which is convex in the momentum. If is the visco…
On the (non) existence of viscosity solutions of multi-time Hamilton-Jacobi equations
Andrea Davini, Maxime Zavidovique
We prove that the multi-time Hamilton-Jacobi equation in general cannot be solved in the viscosity sense, in the non-convex setting, even when the Hamiltonians are in involution.
Aubry sets for weakly coupled systems of Hamilton--Jacobi equations
Andrea Davini, Maxime Zavidovique
We introduce a notion of Aubry set for weakly coupled systems of Hamilton--Jacobi equations on the torus and characterize it as the region where the obstruction to the existence of…
Existence and regularity of strict critical subsolutions in the stationary ergodic setting
Andrea Davini, Antonio Siconolfi
We prove that any continuous and convex stationary ergodic Hamiltonian admits critical subsolutions, which are strict outside the random Aubry set. They make up, in addition, a den…
Weak KAM theoretic aspects for nonregular commuting Hamiltonians
Andrea Davini, Maxime Zavidovique
In this paper we consider the notion of commutation for a pair of continuous and convex Hamiltonians, given in terms of commutation of their Lax- Oleinik semigroups. This is equiva…
Weak KAM Theory topics in the stationary ergodic setting
Andrea Davini, Antonio Siconolfi
We perform a qualitative analysis of the critical equation associated with a stationary ergodic Hamiltonian through a stochastic version of the metric method, where the notion of c…
A metric analysis of critical Hamilton--Jacobi equations in the stationary ergodic setting
Andrea Davini, Antonio Siconolfi
We adapt the metric approach to the study of stationary ergodic Hamilton-Jacobi equations, for which a notion of admissible random (sub)solution is defined. For any level of the Ha…