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．     

一类具有二次自然增长条件的三角形椭圆组弱解的正则性

考虑非线性椭圆组 是有界域 (0.1) 其系数满足下列条件: 当相似文献   

自然增长下的具VMO系数拟线性椭圆组的部分正则性

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.     

自然增长下非线性退化椭圆方程的优化Hlder连续指数

利用Moser-Nash迭代和稠密引理,得到了在自然增长下的非线性退化椭圆方程有界弱解具有某一Hlder指数的正则性;在已知数据的进一步正则性下,建立了具有任意γ满足0≤γ<κ的优化Hlder连续性指数,其中κ是A-调和函数的局部Hlder连续指数.     

p-调和逼近方法和可控增长条件下能量极小p-调和映射的最优内部正则性

考虑能量极小p-调和映射的弱解在可控增长条件下的部分正则性, 结合pp-调和逼近引理和Tan及Yan 在处理退缩椭圆方程组和障碍问题中得到decay估计的方法得到了弱解的部分正则性，并且得到的正则性结果中的指标是最优的.     

具间断系数拟线性退化椭圆方程在可控增长下的正则性

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L^p,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Hlder指数的Hlder连续性结果。     

椭圆型方程的边界正则性与Dini条件

笔者利用Caffarelli扰动方法,证明了Poisson方程和完全非线性一致椭圆型方程在Dini条件下其粘性解的边界正则性,从而给出了文[8]定理4.11不用位势理论的简化证明.     

On the Eigen-value Problem for Elliptic Systems Under Natural Growth Condition: the Super Limit Cases

In this paper, we consider a quasilinear elliptic eigenvalue problem. For the unbounded coefficients, we allow the eigen exponent greater than the Sobolev imbedding critical exponent; for the equations, we also allow the coefficient of suitable smallness condition greater than 1.     

Regularity for a Class of Elliptic Operators with Dini Continuous Coefficients

We obtain regularity results for solutions to Pu=f when P is a kth order elliptic differential operator with the property that both P and P ^t have coefficients that are continuous, with a modulus of continuity satisfying a Dini-type condition. Operators of this form arise in the study of regularity of functions that are known to be regular along the leaves of several foliations, such as arise in Anosov systems. The results here complement some previous results of the author and J. Rauch.     

Fully Nonlinear Parabolic Equations and the Dini Condition

Interior regularity results for viscosity solutions of fully nonlinear uniformly parabolic equations under the Dini condition, which improve and generalize a result due to Kovats, are obtained by the use of the approximation lemma. Received November 21, 2000, Accepted April 27, 2001     

On the Natural Growth Quasilinear Elliptic Euler Equations

In this paper, we consider the eigenvalue problem and the Dirichlet problem of general Euler equations under the natural growth condition.     

次临界增长P-调和组的处处内部正则性

对于低阶梯度项满足次临界增长的p-调和型方程组,本文建立了其弱解梯度具有处处内部H■lder连续性的正则性结果,本文结论就低阶项的增长指标来说已经达到最佳.     

Regularity Results for Nonlinear Systems of Partial Differential Equations Under Weak Ellipticity Conditions

We prove C^{1,α} almost everywhere regularity for weak solutions in the space W^{1,k} (Ω, R^N) of the systems - D_αA^i_α(x,u,Du) = B^i(z,u,Du) under the weak ellipticity condition ∫A(x_0 ,u, p + DΦ) ⋅ DΦdy ≥ λ ∫ (|DΦ|² + |DΦ|^k)dy.