TY - JOUR
T1 - A note on estimates for elliptic systems with L1 data
AU - Raita, Bogdan
AU - Spector, Daniel
N1 - Publisher Copyright:
© 2019 Académie des sciences
PY - 2019/11/1
Y1 - 2019/11/1
N2 - 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=fsubject toCf=0 in Rn to satisfy the estimates ‖Dk−ju‖L [Formula presented] (Rn)⩽c‖f‖L1(Rn) for j∈{1,…,min{k,n−1}} and ‖Dk−nu‖L∞(Rn)⩽c‖f‖L1(Rn) when k≥n.
AB - 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=fsubject toCf=0 in Rn to satisfy the estimates ‖Dk−ju‖L [Formula presented] (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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U2 - 10.1016/j.crma.2019.11.007
DO - 10.1016/j.crma.2019.11.007
M3 - Article
AN - SCOPUS:85075738155
SN - 1631-073X
VL - 357
SP - 851
EP - 857
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 11-12
ER -