广义p调和映照正则性的一个注记

A remark on the regularity of generalized p harmonic maps

广义调和映照(p=2)属于W^(1,q),q>1且其BMO范数很小的时候的正则性由Strzelecki得到.对于广义p调和映照,文中证明了,当p和2很接近的时候,类似的结果也对.其证明主要运用了BMO和H^1的对偶,Hodge分解的稳定性及反Hlder不等式.

The regularity of generalized harmonic maps （p = 2） in W^1,q, q 〉 1 with its BMO norm small was obtained by P Strzelecki. For generalized p harmonic maps, when p is closed to 2, the similar result is proved. The proofs rely on the duality of Hardy space and BMO combined with Lp stability of the Hodge decomposition and reverse HSlder inequalities.