Abstract :
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.
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