Related papers: Hamilton-Jacobi equations with their Hamiltonians …
This paper develops a comparison theorem for viscosity solutions of a new class of Hamilton-Jacobi-Bellman (HJB) equations, which is used to solve the separated problem governed by the K-S equation in the Wasserstein space. A distinctive…
The purpose of this note is to provide an optimal rate of convergence in the vanishing viscosity regime for first-order Hamilton-Jacobi equations with purely quadratic Hamiltonian. We show that for a globally Lipschitz-continuous terminal…
This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order $\alpha \in (0, 1)$ and a Bolza cost functional. The differential game is associated to the…
In this paper we establish H\"older continuity estimates for viscosity solutions to first order Hamilton-Jacobi equations linked to linear control systems satisfying the Kalman rank condition. Our model Hamiltonians are non-convex in the…
The widespread application of modern machine learning has increased the need for robust statistical algorithms. This work studies one such fundamental statistical measure known as the Tukey depth. We study the problem in the continuum…
We give a meaning to the Hamilton--Jacobi equation arising from mean-field spin glass models in the viscosity sense, and establish the corresponding well-posedness. Originally defined on the set of monotone probability measures, these…
We extend the Barles-Perthame procedure of semi-relaxed limits of viscosity solutions of Hamilton-Jacobi equations of the type f - lambda H f = h. The convergence result allows for equations on a `converging sequence of spaces' as well as…
We study the speed of convergence in $L^\infty$ norm of the vanishing viscosity process for Hamilton-Jacobi equations with uniformly or strictly convex Hamiltonian terms with superquadratic behavior. Our analysis boosts previous findings on…
In this paper we study Monge solutions to stationary Hamilton-Jacobi equations associated to discontinuous Hamiltonians in the framework of Carnot groups. After showing the equivalence between Monge and viscosity solutions in the continuous…
We establish existence and uniqueness of minimax solutions for a fairly general class of path-dependent Hamilton-Jacobi equations. In particular, the relevant Hamiltonians can contain the solution and they only need to be measurable with…
A method for finding the general solution to the partial differential equations: \ $F(u_x,u_y)=0$; \ $F(f(x)\:u_x,u_y)=0$ \ (or \ $F(u_x,h(y)\:u_y)=0$) \ is presented, founded on a Legendre like transformation and a theorem for Pfaffian…
We study quantitative large-time averages for Hamilton--Jacobi equations in a dynamic random environment that is stationary ergodic and has unit-range dependence in time. Our motivation comes from stochastic growth models related to the…
We study the nonhomogeneous Dirichlet problem for first order Hamilton-Jacobi equations associated with Tonelli Hamiltonians on a bounded domain $\Omega$ of $\R^n$ assuming the energy level to be supercritical. First, we show that the…
We prove that the viscosity solution to a Hamilton-Jacobi equation with a smooth convex Hamiltonian of the form $H(x,p)$ is differentiable with respect to the initial condition. Moreover, the directional G\^ateaux derivatives can be…
We use the adjoint methods to study the static Hamilton-Jacobi equations and to prove the speed of convergence for those equations. The main new ideas are to introduce adjoint equations corresponding to the formal linearizations of…
This paper provides a counterexample about the asymptotic behavior of the solutions of a discounted Hamilton-Jacobi equation, as the discount factor vanishes. The Hamiltonian of the equation is a 1-dimensional continuous and coercive…
Recently, C. Imbert & R. Monneau study the homogenization of coercive Hamilton-Jacobi Equations with a $u/e$-dependence : this unusual dependence leads to a non-standard cell problem and, in order to solve it, they introduce new ideas to…
This paper investigates the regularity of Lipschitz solutions $u$ to the general two-dimensional equation $\text{div}(G(Du))=0$ with highly degenerate ellipticity. Just assuming strict monotonicity of the field $G$ and heavily relying on…
We consider Hamiltonians associated to optimal control problems for affine systems on the torus. They are not coercive and are possibly unbounded from below in the direction of the drift of the system. The main assumption is the strong…
In this paper, we study the regularity of the ergodic constants for the viscous Hamilton--Jacobi equations. We also estimate the convergent rate of the ergodic constant in the vanishing viscosity process.