Regularity for weakly (K1, K2)-quasiregular mappings

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In this paper, we first give the definition of weakly (K1,K2)-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse Holder inequality, we obtain their regularity property: For any q1 that satisfies 0<K1n(n+4)/22n+1×100n2[23n/2(25n+1)](n - q1) < 1, there exists p1 = p1(n,q1,K1,K2)>n, such that any (K1,K2)-quasiregular mapping f ∈ W1,q1loc(Ω,Rn) is in fact in W1n,p1loc (Ω, Rn). That is, f is (K1, K2)-quasiregular in the usual sense.
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