共查询到19条相似文献,搜索用时 99 毫秒
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本文在较弱的椭圆条件(H_1)和更一般的增长条件(H_5)下,证明了二阶非线性椭圆组弱解的C~(1,σ)-部分正则性. 相似文献
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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. 相似文献
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自然增长下的具VMO系数拟线性椭圆组的部分正则性 总被引:1,自引:0,他引:1
设散度型拟线性系数算子关于自变量x一致满足VMO的结构条件,对于低阶项满足自然增长条件的拟线性椭圆方程组,建立了其弱解具有确切Holder指数的部分正则性. 相似文献
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本文在可控增长条件(1.2)-(1.4)下,对一类非线性椭圆方程组(1.1)改进其很弱解偏微商的可积性,使其为经典意义下的弱解。 相似文献
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对于具有VMO间断系数的散度型拟线性退化椭圆型方程,考虑了低阶项微分项在可控制增长条件下的弱解梯度的Morrey空间Lp,λ局部正则性,从而在已知数据正则性提高的条件下得到弱解具有优化Hlder指数的Hlder连续性结果。 相似文献
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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。 相似文献
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一类非线性椭圆组很弱解的正则性 总被引:3,自引:0,他引:3
本文在可控增长条件(1.2)-(14)下,对一类非线性椭圆方程组(1.1)改进其很弱解偏微商的可积性,使其为经典意义下的弱解. 相似文献
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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. 相似文献
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本文考虑Boussinesq方程一类合适弱解的部分正则性.我们先运用广义能量不等式和奇异积分理论得到一些无维量的估计;再通过合适弱解满足的等式,运用迭代技巧,推导出温度场的小性估计;最后由尺度分析(scaling arguments)得到了一类合适弱解的部分正则性. 相似文献
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Shuhong Chen 《Journal of Mathematical Analysis and Applications》2007,335(1):20-42
In this paper, we consider the nonlinear elliptic systems under controllable growth condition. We 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. We extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition, and directly establishing the optimal Hölder exponent for the derivative of a weak solution. 相似文献
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Shu-hong CHEN & Zhong TAN School of Mathematical Science Xiamen University Xiamen China 《中国科学A辑(英文版)》2007,50(1):105-115
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. 相似文献
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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. 相似文献
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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. 相似文献
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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). 相似文献
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Optimal partial regularity for weak solutions of nonlinear sub-elliptic systems in Carnot groups 总被引:1,自引:0,他引:1
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. 相似文献
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《数学物理学报(B辑英文版)》2020,(3)
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. 相似文献
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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. 相似文献
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Optimal interior partial regularity¶for nonlinear elliptic systems: the method of A-harmonic approximation 总被引:3,自引:0,他引:3
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 相似文献