In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 =...In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 = r2（n, r1,p） 〉 p, such that for every very weak solution u∈W^1r1,loc（Ω） to A-harmonic equation, u also belongs to W^1r2,loc（Ω） . In particular, u is the weak solution to A-harmonic equation in the usual sense.展开更多
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 ...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.展开更多
文摘In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 = r2（n, r1,p） 〉 p, such that for every very weak solution u∈W^1r1,loc（Ω） to A-harmonic equation, u also belongs to W^1r2,loc（Ω） . In particular, u is the weak solution to A-harmonic equation in the usual sense.
基金supported by the Doctor's Foundation of Hebei University
文摘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.
