Methods and Applications of Analysis

Volume 16 (2009)

Number 2

Higher Order Derivative Estimates for Finite-difference Schemes for Linear Elliptic and Parabolic Equations

Pages: 187 – 216



István Gyöngy

Nicolai Krylov


We give sufficient conditions under which solutions of finite-difference schemes in the space variable for second order possibly degenerate linear parabolic and elliptic equations admit estimates of spatial derivatives up to any given order independent of the mesh size.


Finite-difference approximations, linear elliptic, parabolic equations

2010 Mathematics Subject Classification

35J70, 35K65, 65M15

Published 1 January 2009