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

[摘要] 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-Poincare type imbedding theorems and obtain LP-estimates for the gradient operator V and the homotopy operator T from the Banach space L-s(D, Lambda(l)) to the Sobolev space W-l,W-s(D, Lambda(l-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. (c) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-11-15

[关键词] norm inequalities;harmonic equations;differential forms