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 H?lder inequality, we obtain their regularity property: For anyq 1 t...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 H?lder inequality, we obtain their regularity property: For anyq 1 that satisfies $0< K_1 n^{(n + 4)/2} 2^{n + 1} \times 100^{n^2 } [2^{3n/2} (2^{5n} + 1)](n - q_1 )< 1$ , there existsp 1=p 1(n,q 1,K 1,K 2)>n, such that any (K1, K2)-quasiregular mapping $f \in W_{loc}^{1,q_1 } (\Omega ,R^n )$ is in fact in $W_{loc}^{1,p_1 } (\Omega , R^n )$ . That is, f is (K1,K2)-quasiregular in the usual sense.展开更多
For the generalized Beltrami system with two characteristic matrices, we deal with the regularity of its very weak solutions in the Sobolev class (1 < r < n). By changing the generalized Beltrami system into a ...For the generalized Beltrami system with two characteristic matrices, we deal with the regularity of its very weak solutions in the Sobolev class (1 < r < n). By changing the generalized Beltrami system into a class of a divergent elliptic system with nonhomogeneous items, we obtain that each of its very weak solutions is essentially a classical weak solution of a usual Sobolev class. Furthermore, we also establish a higher regularity of its weak solution if the regularity hypotheses of two characteristic matrices are improved.展开更多
In this paper we establish an interior regularity of weak solution for quasi-linear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the varia...In this paper we establish an interior regularity of weak solution for quasi-linear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the variable x uniformly with respect to all u, and the lower order item B（x, u, △↓u） satisfies the subcritical growth （1.2）. In particular, when F（x） ∈ L^q（Ω） and f（x） ∈ L^γ（Ω） with q,γ 〉 for any 1 〈 p 〈 ＋∞, we obtain interior HSlder continuity of any weak solution of （1.1） u with an index κ = min{1 - n/q, 1 - n/γ}.展开更多
In this paper we establish some new dynamic inequalities on time scales which contain in particular generalizations of integral and discrete inequalities due to Hardy, Littlewood, Polya, D＇Apuzzo, Sbordone and Popoli...In this paper we establish some new dynamic inequalities on time scales which contain in particular generalizations of integral and discrete inequalities due to Hardy, Littlewood, Polya, D＇Apuzzo, Sbordone and Popoli. We also apply these inequalities to prove a higher integrability theorem for decreasing functions on time scales.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 H?lder inequality, we obtain their regularity property: For anyq 1 that satisfies $0< K_1 n^{(n + 4)/2} 2^{n + 1} \times 100^{n^2 } [2^{3n/2} (2^{5n} + 1)](n - q_1 )< 1$ , there existsp 1=p 1(n,q 1,K 1,K 2)>n, such that any (K1, K2)-quasiregular mapping $f \in W_{loc}^{1,q_1 } (\Omega ,R^n )$ is in fact in $W_{loc}^{1,p_1 } (\Omega , R^n )$ . That is, f is (K1,K2)-quasiregular in the usual sense.
基金Supported by the National Natural Science Foundation of China(49805005)by the research foundation of Northern Jiaotong University(2002SM061).
文摘For the generalized Beltrami system with two characteristic matrices, we deal with the regularity of its very weak solutions in the Sobolev class (1 < r < n). By changing the generalized Beltrami system into a class of a divergent elliptic system with nonhomogeneous items, we obtain that each of its very weak solutions is essentially a classical weak solution of a usual Sobolev class. Furthermore, we also establish a higher regularity of its weak solution if the regularity hypotheses of two characteristic matrices are improved.
基金National Natural Science Foundation of China (No.10671022)
文摘In this paper we establish an interior regularity of weak solution for quasi-linear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the variable x uniformly with respect to all u, and the lower order item B（x, u, △↓u） satisfies the subcritical growth （1.2）. In particular, when F（x） ∈ L^q（Ω） and f（x） ∈ L^γ（Ω） with q,γ 〉 for any 1 〈 p 〈 ＋∞, we obtain interior HSlder continuity of any weak solution of （1.1） u with an index κ = min{1 - n/q, 1 - n/γ}.
文摘In this paper we establish some new dynamic inequalities on time scales which contain in particular generalizations of integral and discrete inequalities due to Hardy, Littlewood, Polya, D＇Apuzzo, Sbordone and Popoli. We also apply these inequalities to prove a higher integrability theorem for decreasing functions on time scales.
