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.     

Partial regularity for weak solutions of stationary navier-stokes systems

This article is concerned with the partial regularity for the weak solutions of stationary Navier-Stokes system under the controllable growth condition.By A-harmonic approximation technique,the optimal regularity is obtained.     

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. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10531020) and the Program of 985 Innovation Engineering on Information in Xiamen University (2004–2007).     

Optimal partial regularity of second order parabolic systems under controllable growth condition

We consider the regularity for weak solutions of second order nonlinear parabolic systems under controllable growth condition, and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, we get the optimal regularity by the method of A-caloric approximation introduced by Duzaar and Mingione.     

Optimal partial regularity for weak solutions of nonlinear sub-elliptic systems in Carnot groups

This paper is concerned with partial regularity for weak solutions to nonlinear sub-elliptic systems in divergence form in Carnot groups. The technique of A-harmonic approximation introduced by Simon and developed by Duzaar and Grotowski is adapted to our context. We establish Caccioppoli type inequalities and partial regularity with optimal local Hölder exponents for horizontal gradients of weak solutions to systems under super-quadratic natural structure conditions and super-quadratic controllable structure conditions, respectively.     

PARTIAL REGULARITY FOR STATIONARY NAVIER-STOKES SYSTEMS BY THE METHOD OF A-HARMONIC APPROXIMATION

In this article, we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition. The proof is based on the A-harmonic approximation technique. In this article,we extend the result of Shuhong Chen and Zhong Tan [7] and Giaquinta and Modica [18] to the stationary Navier-Stokes system with subquadratic growth.     

PARTIAL REGULARITY OF STATIONARY NAVIER-STOKES SYSTEMS UNDER NATURAL GROWTH CONDITION

In this article, we consider the partial regularity of stationary Navier-Stokes system under the natural growth condition. Applying the method of A-harmonic approximation,we obtain some results about the partial regularity and establish the optimal Holder exponent for the derivative of a weak solution on its regular set.     

Optimal interior partial regularity¶for nonlinear elliptic systems: the method of A-harmonic approximation

We consider nonlinear elliptic systems of divergence type. We provide a new method for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. This method is applied to both homogeneous and inhomogeneous systems, in the latter case with inhomogeneity obeying the natural growth condition. Our methods extend previous partial regularity results, directly establishing the optimal H?lder exponent for the derivative of a weak solution on its regular set. We also indicate how the technique can be applied to further simplify the proof of partial regularity for quasilinear elliptic systems. Received: 22 July 1999 / Revised version: 23 May 2000     

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．     

The method of <Emphasis Type="Italic">A</Emphasis>-harmonic approximation and boundary regularity for nonlinear elliptic systems under the natural growth condition

We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.     

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS UNDER THE NATURAL GROWTH CONDITION： THE METHOD OF A-HARMONIC APPROXIMATION

In this article,the authors consider the nonlinear elliptic systems under the natural growth condition.They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions,based on a generalization of the technique of harmonic approximation.And directly establish the optimal Holder exponent for the derivative of a weak solution.     

Everywhere Regularity for Weak Solutions to Variational Inequalities of Triangular Form

In this paper, we obtain two results of weak solutions to variational inequalities of triangular form under controllable growth and a class of natural growth conditions, i.e. 1^°. L^p-estimate for the gradient; 2^°. C^{1,β}_{loc}(Ω, R^N) regularity.     

Partial regularity for degenerate subelliptic systems associated with Hörmander’s vector fields

The paper is devoted to partial Hölder estimates for weak solutions of a class of degenerate subelliptic systems constructed by Hörmander’s vector fields. Assumptions on the systems are that coefficient matrix satisfies VMO condition in the sense of Carnot-Carathéodory distance in variables x for fixed u, and lower order terms satisfy the natural growth condition and the controllable growth condition, respectively.     

Optimal partial regularity of second order nonlinear elliptic systems with Dini continuous coefficients for the superquadratic case

We consider the regularity for weak solutions of second order nonlinear elliptic systems with Dini continuous coefficients for the superquadratic case under natural growth condition, and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal Hölder exponent for the derivative of the weak solutions on the regular set.     

Optimal partial regularity for sub-elliptic systems with sub-quadratic growth in Carnot groups

This paper is devoted to partial regularity for weak solutions to nonlinear sub-elliptic systems for the case 1<m<2 under natural growth conditions in Carnot groups. The method of A-harmonic approximation introduced by Simon and developed by Duzaar, Grotowski and Kronz is adapted to our context, and then partial regularity with the optimal local Hölder exponent for horizontal gradients of weak solutions to the systems is established.     

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.     

Partial Hölder regularity for elliptic systems with non-standard growth

We study partial Hölder regularity for elliptic systems with non-standard growth. We consider general systems with Orlicz growth and discontinuous coefficient factor, for which we prove that their weak solutions are partially Hölder continuous for any Hölder exponents. In addition, we also obtain a similar result for systems with double phase growth.     

A new partial regularity proof for solutions of nonlinear elliptic systems

We prove partial regularity for weak solutionsu of the fully nonlinear elliptic system divA (x, u, Du) +B (x, u, Du)=0, whereA andB have natural polynomial growth, and whereB satisfies a two-sided or a one-sided condition. We do not employ a reverse Hölder inequality.     

R~3中各向异性Landau-Lifshitz方程的部分正则解

证明了当三维空间中各向异性Landau-Lifshitz方程的弱解满足稳定性条件时,其解具有部分正则性,并且对易面类型的方程,利用Ginzburg-Landau逼近构造了一个整体的部分正则解。