A-调和逼近方法和具有可控增长条件的非线性椭圆方程组最优内部部分正则性

考虑具有可控增长条件的非线性椭圆方程组弱解的部分正则性．利用Duzaar和Grotowski引进的弱解部分正则性证明的新方法，该方法是建立在调和逼近技巧一般形式的基础上的，我们把前人的结果由自然增长条件推广到了可控增长条件，并且所得到的弱解导数的Hoelder指标是最优的．     

The method of p-harmonic approximation and optimal interior partial regularity for energy minimizing p-harmonic maps under the controllable growth condition

In this paper, we are concerned with the partial regularity for the weak solutions of energy minimizing p-harmonic maps under the controllable growth condition. We get the interior partial regularity by the p-harmonic approximation method together with the technique used to get the decay estimation on some Degenerate elliptic equations and the obstacle problem by Tan and Yan. In particular, we directly get the optimal regularity.     

Hölder Regularity for Nonhomogeneous Elliptic Systems with Nonlinearity Greater than Two

Regularity results for elliptic systems of second order quasilinear PDEs with nonlinear growth of order q > 2 are proved, extending results of [7] and [10]. In particular Hölder regularity of the solutions is obtained if the dimension n is less than or equal to q + 2.     

具有Dini连续性系数的非线性椭圆方程组在自然增长条件下的最优内部部分正则性

本文我们研究的是具有Dini连续性系数的散度形式的非线性椭圆方程组在自然增长条件下的问题．我们证明所用的方法是有Dugaar和Grotowski所引进的调和逼近技巧。这种技窍在证明弱解的局部正则性时非常重要．我们可以用之直接得到最优局部正则性结果．     

On Regularity for Beurling–Deny Type Dirichlet Forms

Characteristic examples of Beurling–Deny type Dirichlet forms are considered. The forms are identified with bilinear forms of integro-differential operators that arise as generators of jump-diffusion processes. The aim of this article is to prove Harnack inequalities for these operators and consequently Hölder regularity of weak H ¹-solutions. Moser's iteration technique is used.     

Regularity of Solutions of the Cahn-Hilliard Equation with Non-constant Mobility

In this paper, we study the regularity of solutions for two-dimensional Cahn-Hilliard equation with non-constant mobility. Basing on the L^p type estimates and Schauder type estimates, we prove the global existence of classical solutions.     

The Cauchy Problem for the Generalized Korteweg-de Vries-Benjamin-Ono Equation with Low Regularity Data

The Cauchy problem of the generalized Korteweg-de Vries-Benjamin-Ono equation is considered, and low regularity and limit behavior of the solutions are obtained. For k = 1, local well- posedness is obtained for data in H^s（R）（s 〉 -3/4）. For k = 2, local result for data in H^S（R）（s 〉1/4） is obtained. For k = 3, local result for data in H^S（R）（s 〉 -1/6） is obtained. Moreover, the solutions of generalized Korteweg-de Vries-Benjamin-Ono equation converge to the solutions of KdV equation if the term of Benjamin-Ono equation tends to zero.     

Some New Regularity Criteria for the Navier-Stokes Equations Containing Gradient of the Velocity

We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.     

高维Lienard型方程的调和解

本文运用重合度理论，在阻尼可负的条件下，得到Ｌｉｅｎａｒｄ型系统存在调和解的若干新判据。     

Regularity for nonlinear elliptic systems with dini coefficients under natural growth condition for the case: 1 < m < 2

In this article, we consider interior regularity for weak solutions to nonlinear elliptic systems of divergence type with Dini continuous coefficients under natural growth condition for the case 1 < m < 2. All estimates in the case of m ≥ 2 is no longer suitable, and we can't obtain the Caccioppoli's second inequality by using these techniques developed in the case of m ≥ 2. But the Caccioppoli's second inequality is the key to use A-harmonic approximation method. Thus, we adopt another technique introduced by Acerbi and Fcsco to overcome the difficulty and we also overcome those difficulties due to Dini condition. And then we apply the A-harmonic approximation method to prove partial regularity of weak solutions.