相关论文: On the regularizing effect for unbounded solutions…
We examine Hamilton-Jacobi equations driven by fully nonlinear degenerate elliptic operators in the presence of superlinear Hamiltonians. By exploring the Ishii-Jensen inequality, we prove that viscosity solutions are locally…
We prove well-posedness for some abstract differential equations of the first order. Our result covers the usual case of Lipschitz composition operators. It also contains the case of some integro-differential operators acting on spaces with…
We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems. This point of view is illustrated on the problem of inference of a rank-one matrix.…
In this paper we study the regularity of viscosity solutions to the following Hamilton-Jacobi equations $$ \partial_t u + H(D_{x} u)=0 \qquad \textrm{in} \Omega\subset \mathbb R\times \mathbb R^{n} . $$ In particular, under the assumption…
The time dependent Eikonal equation is a Hamilton-Jacobi equation with Hamiltonian $H(P)=|P|$, which is not strictly convex nor smooth. The regularizing effect of Hamiltonian for the Eikonal equation is much weaker than that of strictly…
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 uniformly convex Hamiltonian. We prove that for a globally Lipschitz-continuous and…
This paper is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity…
Motivated by optimal control problems and differential games for functional differential equations of retarded type, the paper deals with a Cauchy problem for a path-dependent Hamilton--Jacobi equation with a right-end boundary condition.…
This paper is concerned with the quantitative homogenization of the steady Stokes equations with the Dirichlet condition in a periodically perforated domain. Using a compactness method, we establish the large-scale interior $C^{1, \alpha}$…
We prove two H\"older regularity results for solutions of generated Jacobian equations. First, that under the A3 condition and the assumption of nonnegative $L^p$ valued data solutions are $C^{1,\alpha}$ for an $\alpha$ that is sharp. Then,…
We consider the non-linear equation $T^{-1} u+\partial_tu-\partial_x^2\pi(u)=\xi$ driven by space-time white noise $\xi$, which is uniformly parabolic because we assume that $\pi'$ is bounded away from zero and infinity. Under the further…
We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…
In this paper, we are concerned with the classical solvability of a class of second-order Hamilton-Jacobi-Bellman equations (HJB equations) arising from stochastic optimal control problems with linear dynamics and uniformly convex cost…
We study the doubly nonlinear PDE $$ |\partial_t u|^{p-2}\,\partial_t u-\textrm{div}(|\nabla u|^{p-2}\nabla u)=0. $$ This equation arises in the study of extremals of Poincar\'e inequalities in Sobolev spaces. We prove spatial Lipschitz…
We study the regularity properties of integro-partial differential equations of Hamilton-Jocobi-Bellman type with terminal condition, which can be interpreted through a stochastic control system, composed of a forward and a backward…
This paper deals with the regularity of solutions of the Hamilton-Jacobi Inequality which arises in H-infinity control. It shows by explicit counterexamples that there are gaps between existence of continuous and locally Lipschitz (positive…
The purpose of this work is twofold. First we study the solutions of a Hamilton-Jacobi equation of the form $u_t(t,x)+\mathcal{H}(t,x,\nabla_H u(t,x))=0$, where $\nabla_H u$ represents the horizontal gradient of a function $u$ defined on…
We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point,…
Let $2\le n\le9$. Suppose that $f:R\to R$ is locally Lipschitz function satisfying $f(t)\ge A\min\{0,t\}-K$ for all $t\in R$ with some constant $A\ge0$ and $K\ge 0$. We establish an a priori interior H\"older regularity of $C^2$-stable…
In this paper we study Liouville-type properties for a class of degenerate elliptic equations driven by the fractional infinity Laplacian with nonlinear lower-order terms, \[ \Delta_\infty^{\beta}u - c\,H(u,\nabla u) - \lambda\, f(|x|,u)=0…