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 toAu=fsubject toCf=0 in Rnto satisfy the estimates‖Dk−ju‖Lnn−j(Rn)⩽c‖f‖L1(Rn)for j∈{1,…,min{k,n−1}} and‖Dk−nu‖L∞(Rn)⩽c‖f‖L1(Rn)when k≥n.
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