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, 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 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
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}.
基金Supported by NSFC(No.11671031,No.11471018)the Fundamental Research Funds for the Central Universities(No.FRF-TP-14-005C1)+1 种基金Program for New Century Excellent Talents in Universitythe Beijing Natural Science Foundation(No.1142005)
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.
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.
