Ar(Ω)-weighted inequalities for A-harmonic tensors and related operators

We first prove the local Ar(Ω)-weighted Poincaré inequality for A-harmonic tensors on domain Ω and the analogue for the projection operator. Then, we prove the global Ar(Ω)-weighted Poincaré inequality for A-harmonic tensors. Finally, using the global Ar(Ω)-weighted inequality established for A-harmonic tensors, we obtain the global Ar(Ω)-weighted Poincaré inequality for the projection operator. © 2005 Elsevier Inc. All rights reserved