Local and global norm comparison theorems for solutions to the nonhomogeneous A-harmonic equation

We establish local and global norm inequalities for solutions of the nonhomogeneous A-harmonic equation A(x, g + du) = h + d v for differential forms. As applications of these inequalities, we prove the Sobolev–Poincaré type imbedding theorems and obtain Lp-estimates for the gradient operator ∇ and the homotopy operator T from the Banach space Ls(D,Λl ) to the Sobolev spaceW1,s(D,Λl−1), l = 1, 2, . . . , n. These results can be used to study both qualitative and quantitative properties of solutions of the A-harmonic equations and the related differential systems. © 2007 Elsevier Inc. All rights reserved.