A note on estimates for elliptic systems with L1 data
Bogdan Raiţă, Daniel Spector · Comptes Rendus Mathématique · 2019
In this paper, we give necessary and sufficient conditions on the compatibility of a k th-order homogeneous linear elliptic differential operator A and differential constraint C for solutions to A u = f subject to C f = 0 in R n to satisfy the estimates ‖ D k − j u ‖ L n n − j ( R n ) ⩽ c ‖ f ‖ L 1 ( R n ) for j ∈ { 1 , … , min { k , n − 1 } } and ‖ D k − n u ‖ L ∞ ( R n ) ⩽ c ‖ f ‖ L 1 ( R n