共查询到18条相似文献,搜索用时 62 毫秒
1.
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
2.
讨论了具间断系数的N维拟线性椭圆方程. 利用估计和差分逼近方法,证明了弱解的一阶导数H\"{o}lder连续到方程系数间断的内边界. 相似文献
3.
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
4.
讨论了具特殊主部和线性增长系数的n维拟线性抛物挠射问题,利用估计和平均函数方法,证明了弱解在内边界附近的一些正则性质.把这些正则性结果从线性问题推广到这种拟线性问题. 相似文献
5.
本文研究Heisenberg群上具有VMO(零平均振荡)系数的非散度型退化椭圆方程.通过证明适当的Sobolev-Poincaré型不等式,建立方程的Lp正则性;然后利用初等方法,得到退化椭圆方程解的Morrey正则性. 相似文献
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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
8.
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
9.
用变分方法研究了半线性椭圆方程Dirichlet迫值同题-△μ=f(x,μ) h(x)对几乎所有的x∈Ω,μ=0在δΩ上解的存在性,在临界增长情况下得到了所解的一个存在性定理. 相似文献
10.
张文丽 《数学的实践与认识》2014,(21)
研究了一类含Sobolev临界指数的p-Laplacian奇异拟线性椭圆方程组,利用变分方法,结合Nehari流形和集中紧性原理证明对应的能量泛函满足局部(PS)条件,得到了这一方程组正基态解的存在性. 相似文献
11.
YeMinCHEN 《数学学报(英文版)》2004,20(6):1103-1118
The aim of this paper is to study the regularity of solutions to the Dirichlet problems for general second-order elliptic equations in Lebesgue and Morrey spaces. We consider both nondivergence and divergence forms and the coefficients of principle terms are assumed to be in VMO. 相似文献
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The paper investigates the partial regularity of the minimizersfor quadratic functionals whose integrands have VMO coefficientsin principal part and nonlinear terms that are Carathéodoryfunctions. We use some majorizations for the functional, ratherthan the well known Euler equation associated to it. 相似文献
13.
N. V. Krylov 《偏微分方程通讯》2013,38(3):453-475
An Lp-theory of divergence and non-divergence form elliptic and parabolic equations is presented. The main coefficients are supposed to belong to the class VMOx, which, in particular, contains all functions independent of x. Weak uniqueness of the martingale problem associated with such equations is obtained. 相似文献
14.
In this paper, by means of the theories of singular integrals and linear commutators, the authors establish the regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients. 相似文献
15.
We show continuity in generalized Morrey spaces of sublinear integral operators generated by Calderón-Zygmund operator and their commutators with BMO functions. The obtained estimates are used to study global regularity of the solution of the Dirichlet problem for linear uniformly elliptic operators. 相似文献
16.
Davide Guidetti 《Mathematische Nachrichten》2002,237(1):62-88
We prove a priori estimates in Sobolev spaces for general linear elliptic boundary value problems with VMO coefficients.We give also results of existence and uniqueness of a solution. 相似文献
17.
证明了拟线性次椭圆方程组-X_α~*(a_(ij)~(αβ)(x,u)X_βu~j)=-X_α~*f_i~α+g_i,i=1,2,…,N,x∈Ω的弱解广义梯度Xu在Morrey空间L_x~(p,λ)(Ω,R~(mN))(p2)上的部分正则性,其中光滑实向量场族X=(X_1,X_2,…,X_m)满足H(o|¨)rmander有限秩条件,X_α~*是X_α的共轭;而且主项系数a_(ij)~(αβ)(x,u)关于x一致VMO(Vanishing Mean Oscillation的缩写,消失平均震荡)间断,且关于u为一致连续. 相似文献
18.
We study the obstacle problem with an elliptic operator in nondivergence form with principal coefficients in VMO. We develop all of the basic theory of existence, uniqueness, optimal regularity, and nondegeneracy of the solutions. These results, in turn, allow us to begin the study of the regularity of the free boundary, and we show existence of blowup limits, a basic measure stability result, and a measure-theoretic version of the Caffarelli alternative proven in [3]. 相似文献