Related papers: A priori estimates of smoothness of solutions to d…

We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…

In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a…

The representation of the solution of some Backward Stochastic Differential Equation as an infinite series is obtained. Some exactly solvable examples are considered.

The method of constructing approximate solutions of the first boundary value problem for linear differential equations based on incomplete (even and odd) trigonometric splines is considered. The theoretical positions are illustrated by…

We present a finite difference method to compute the principal eigenvalue and the corresponding eigenfunction for a large class of second order elliptic operators including notably linear operators in nondivergence form and fully nonlinear…

We study the rate of convergence of an explicit and an implicit-explicit finite difference scheme for linear stochastic integro-differential equations of parabolic type arising in non-linear filtering of jump-diffusion processes. We show…

We give an example of quasiderivatives constructed by random time change, Girsanov's Theorem and Levy's Theorem. As an application, we investigate the smoothness and estimate the derivatives up to second order for the probabilistic solution…

This article presents a comprehensive overview and supplement to recent developments in second-order elliptic partial differential equations formulated in double divergence form, along with an exploration of their parabolic counterparts.

We show that a certain error estimate for a fully discrete finite element approximation of the solution of the heat equation which is defined in a two-dimensional Euclidean domain carries over to the case of a general linear parabolic…

This paper studies a priori and regularity estimates of Evans-Krylov type in H\"older spaces for fully nonlinear uniformly elliptic and parabolic equations of second order when the operator fails to be concave or convex in the space of…

We compute the rate of convergence of forward, backward and central finite difference $\theta$-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and…

Error estimation of difference operators on irregular nodes is discussed. We can obtain the similar estimates of the errors. However, the error estimate for the difference operators for the second derivatives becomes lower because 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…

Explicit numerical methods based on Lax-Friedrichs and Leap-Frog finite difference approximations are constructed to find the numerical solution of the first-order hyperbolic partial differential equation with point-wise delay or advance,…

In this paper, we obtain a priori estimates for the set of anti-symmetric solutions to a fractional Laplacian equation in a bounded domain using a blowing-up and rescaling argument. In order to establish a contradiction to possible…

By using some deep tools from microlocal analysis, the authors of the papers (Ann. of Math., 165 (2007), 567--591, J. Amer. Math. Soc., 23 (2010), 655--691; Invent. Math., 178 (2009), 119--171; Duke Math. J., 158(2011), 83--120) have…

We establish a priori Lipschitz estimates for unbounded solutions of second-order Hamilton-Jacobi equations in R^N in presence of an Ornstein-Uhlenbeck drift. We generalize the results obtained by Fujita, Ishii \& Loreti (2006) in several…

We establish a new sharp estimate of the order of vanishing of solutions to parabolic equations with variable coefficients. For real-analytic leading coefficients, we prove a localised estimate of the nodal set, at a given time-level, that…

In this paper, we propose a second-order dynamical system with a smoothing effect for solving paramonotone variational inequalities. Under standard assumptions, we prove that the trajectories of this dynamical system converges to a solution…

We prove L^p estimates for a class of two-dimensional multilinear forms that naturally generalize (dyadic variants of) both classical paraproducts and the twisted paraproduct introduced in [5] and studied in [1] and [6]. The method we use…