Maximal regularity of parabolic equations associated with a discrete Laplacian

Let d be the discrete Laplacian defined on Zd by setting df (n ) = d j=1 -[f (n +e j) + f (n - e j)- 2f (n ), n is an element of Zd, where {e j : j = 1, ... , d} is the standard basis for Rd. In this paper, we prove weighted mixed norm estimates and end-point estimates for the maximal regularity of the discrete parabolic equation 1 ut +du = f, t is an element of [0, T ) u(0, center dot) =0, where T is an element of (0, infinity). (c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).