Regularity for weakly (K_1, K_2)-quasiregular mappings

摘要

In this paper, we first give the definition of weakly (K_1, K_2)-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse Hoelder inequality, we obtain their regularity property: For any q_1 that satisfies 0 < K_1n~((n+4)/2)2~(n+1) X 100~(n~2) [2~(3n/2)(2~(5n) + 1)](n - q_1) < 1, there exists p_1 = p_1 (n, q_1,K_1, K_2) > n, such that any (K_1, K_2-quasiregular mapping f ∈ W_(loc)~(1,q_1)(Ω, R~n) is in fact in W_(loc)~(1,q_1)(Ω, R~n). That is, f is (K_1, K_2)-quasiregular in the usual sense.