A-调和逼近技巧与非线性椭圆方程组的部分正则性  

A-harmonic Approximation Technique and Partial Regularity for Nonlinear Elliptic Systems

作　　者：谭忠[1] 林慧[1] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2004年第4期429-431,共3页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10171083)资助

摘　　要：应用一个新方法,即用A 调和逼近技巧考虑了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.改进了以往部分正则性的结果,直接建立了弱解的导数在正则集上的最优H lder指标,结果的证明主要是将A 调和逼近引理与第2Caccioppoli不等式巧妙结合起来.首先,证明g=u-p0(x-x0)γ(γ是某常数)满足A 调和逼近引理中g的性质,于是找到一个具有许多好性质的A 调和函数h.从而对g的梯度的L2模估计通过第2Caccioppoli不等式变为对g本身的L2估计,再应用A 调和逼近引理转化对A 调和函数h的估计,进而得到了正则性所要的标准估计式.The partial regularity for nonlinear elliptic systems with controllable growth conditions is considered. Here a new method is applied: A-harmonic approximation technique and extend previous partial regularity results, directly establishing the optimal Hlder exponent for the derivative of a weak solution on its regular set.The proof of the result is to skillfully combine A-harmonic approximation Lemma and Caccioppoli's second inequality. First, g=u-p_0(x-x_0)γis proved( where γ is some constant) which satisfiesg's property in A-harmonic approximation Lemma. And an A-harmonic functionh with many good properties is found. So through Caccioppoli's second inequality,L^2-estimate forg's gradient is transformed to estimateL^2 ofg. Furthermore, by applying A-harmonic approximation Lemma to estimate the A-harmonic functionh, the standard estimate for partial regularity is obstained.

关 键 词：A-调和逼近技巧 非线性椭圆方程组 部分正则性 最优Hǒlder指标 梯度矩阵 

分 类 号：O175.25[理学—数学]