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Local and global norm comparison theorems for solutions to the nonhomogeneous A-harmonic equation
Authors:Shusen Ding
Institution:Department of Mathematics, Seattle University, Seattle, WA 98122, USA
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 space W1,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.
Keywords:Norm inequalities  Harmonic equations  Differential forms
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