Related papers: Error bounds for monotone approximation schemes fo…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
In this paper we prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of epsilon. The main…
We obtain an error estimate between viscosity solutions and \delta-viscosity solutions of nonhomogeneous fully nonlinear uniformly elliptic equations. The main assumption, besides uniform ellipticity, is that the nonlinearity is…
Variational inequalities represent a broad class of problems, including minimization and min-max problems, commonly found in machine learning. Existing second-order and high-order methods for variational inequalities require precise…
We investigate error bounds for numerical solutions of divergence structure linear elliptic PDEs on compact manifolds without boundary. Our focus is on a class of monotone finite difference approximations, which provide a strong form of…
Aim of this paper is to extend the continuous dependence estimates proved in \cite{JK1} to quasi-monotone systems of fully nonlinear second-order parabolic equations. As by-product of these estimates, we get an H\"older estimate for bounded…
The author presented a stochastic and variational approach to the Lax-Friedrichs finite difference scheme applied to hyperbolic scalar conservation laws and the corresponding Hamilton-Jacobi equations with convex and superlinear…
This paper is concerned with quantitative homogenization of second-order parabolic systems with periodic coefficients varying rapidly in space and time, in different scales. We obtain large-scale interior and boundary Lipschitz estimates as…
We prove that the effective nonlinearities (ergodic constants) obtained in the stochastic homogenization of Hamilton-Jacobi, "viscous" Hamilton-Jacobi and nonlinear uniformly elliptic pde are approximated by the analogous quantities of…
In this work we develop a new numerical approach for recovering a spatially dependent source component in a standard parabolic equation from partial interior measurements. We establish novel conditional Lipschitz stability and H\"{o}lder…
We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…
We propose an approximation scheme for a class of semilinear parabolic equations that are convex and coercive in their gradients. Such equations arise often in pricing and portfolio management in incomplete markets and, more broadly, are…
This paper develops a new framework for designing and analyzing convergent finite difference methods for approximating both classical and viscosity solutions of second order fully nonlinear partial differential equations (PDEs) in 1-D. The…
It is often the case in numerical relativity that schemes that are known to be convergent for well posed systems are used in evolutions of weakly hyperbolic (WH) formulations of Einstein's equations. Here we explicitly show that with…
We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a…
We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…
We propose an approximation scheme for a class of semilinear variational inequalities whose Hamiltonian is convex and coercive. The proposed scheme is a natural extension of a previous splitting scheme proposed by Liang, Zariphopoulou and…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
In this work, we deal with approximations for distribution functions of non-negative random variables. More specifically, we construct continuous approximants using an acceleration technique over a well-know inversion formula for Laplace…
We present a local almost everywhere regularity result for a general nonlinear non-diagonal parabolic system, which main part depends on symmetric part of the gradient.