A note on estimates for elliptic systems with L-1 data

Abstract

In this paper, we give necessary and sufficient conditions on the compatibility of a kth-order homogeneous linear elliptic differential operator A and differential constraint C for solutions to Au = f subject to Cf = 0 in R-n to satisfy the estimates parallel to D(k-j)u parallel to(Ln/n-j(Rn)) <= c parallel to f parallel to(L1(Rn)) for j is an element of {1, ..., min{k, n-1}} and parallel to D(k-n)u parallel to(L infinity(Rn)) <= c parallel to f parallel to(L1(Rn)) when k >= n. (C) 2019 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.