Regularity Of Degenerate Weakly (L₁, L₂)-BLD Mappings

In this paper, we first give the definition of degenerate weakly (L1, L2) - BLD mappings and degenerate weakly (K1, K2) - qusiregular mappings in space, and relation of the two mappings. What is the smallest number q1 in the regularity of qusiregular mappings and BLD mappings, that is our most care about, so by using the technique of Hodge decomposition and weakly reverse Holder inequality , we prove the following regularity result of degenerate weakly (L1, L2) - BLD mappings : for every q1 such that 0 < < 1 there exist integrable exponent p1 = p1(n, l, q1, L1; L2) > l, such that for every degenerate weakly (L1,L2) - BLD mapping f W ( ,Rn), we have f W ( ,Rn) , that is , f is a degenerate (L1, L2) - BLD mapping in the usual sense.