本文给出空间退化的弱(L1,L2)-BLD映射的定义.利用Hodge分解,弱逆Holder不等式等工具,证明了其正则性结果:对任意满足Ol,使得对任意退化的弱(L1,L2)-BLD映射f∈Wloc1,q1(Ω,Rn),都有f∈Wloc1,p1(Ω,Rn),即f为通常意义下的退化的(L1,L2)-BLD映射.

In this paper, we give the definition of degenerate weak (L1, L2)-BLD map-pings in space, and by using the technique of Hodge decomposition and weakly reverse Holder inequality we prove the following regularity result of degenerate weak (L1,L2)-BLD mappings: For every q1 such that 0< L2lnl/2l221+l×100n2[23l/2(24l+n+1)](l-q1) < 1 there exists integrable exponent p1 = p1(n,l,q1,L1,L2) >, such that every degenerate weak (L1,L2)-BLD mapping f∈Wloc1,q1(Ω,Rn) belongs to Wloc1,p1(Ω,Rn), that is, f is a degenerate (L1,L2)-BLD mapping in the usual sense.