自然增长条件下的非齐次A-调和方程弱解的梯度估计

该文主要研究一类自然增长条件下的非齐次A-调和方程弱解的梯度估计,首先获得自然增长条件下的非齐次A-调和方程弱解的L^p估计,然后使用迭代覆盖逼近等方法,将其推广到Orlicz空间.     

加权BMO函数空间上的Hardy—Littlewood极大算子

本文给出了Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ极大函数的加权ＢＭＯ的有界性证明，即若ｆ∈ＢＭＯ，Ｗ∈Ａ∞且ｉｎｆｍｆ（ｘ）〈∞则Ｍ（ｆ）（ｚ）∈ＢＭＯ。     

具有BMO系数的拟线性椭圆方程解的BMO估计

We establish a global limiting case of nonlinear Calderon-Zygmund theory to quasilinear elliptic equations div A(x,Du) = div(|F|~(p-2)F) under the BMO smallness of the nonlinearity,that is |F|~(p-2)F∈BMO implies that Du ∈BMO.     

核满足弱正则条件的多线性算子交换子的加权估计

本文主要研究核满足弱正则条件的算子与BMO函数生成的多线性交换子.建立了多线性交换子在加权Lebesgue空间的一些性质.     

强奇异Calderón-Zygmund算子的交换子的双权BMO估计

研究了由强奇异Calderón-Zygmund算子T和加权BMO（ω）函数b生成的交换子Tb的sharp极大函数的点态估计,证明了这类交换子是由L^[p]（μ）到LP（μ）到LP（υ）上的有界算子,其中ω=（μυ^[-1]）^[1/P]且μυ∈Ap,1〈P〈∞．     

自然增长的半线性次椭圆方程内部H?lder估计

对于低阶项满足自然增长条件的半线性次椭圆方程有界弱解,通过Moser-Nash迭代和弱Harnack不等式,得到弱解的内部H?lder连续性估计.     

加权BMO函数空间上的Hardy－Littlewood极大算子

本文给出了Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ极大函数和加权ＢＭＯ的有界性证明：即若f∈ＢＭＯ_w,w∈A_∞,且(?)Mf(x)<∞, 则M(f)(x) ∈BMO_w, 且‖Mf‖_w^*≤c‖f‖_w^*.     

齐型空间上的极大算子的BMO有界性

本文完全解决了满足条件“所有开球都是开集且连续函数全体在Ｌ¹中稠”的齐型空间上的Ｈ－Ｌ极大算子的ＢＭＯ有界性。     

极大函数交换子在广义Morrey空间的估计

主要讨论了Hardy-Littlewood极大函数,Sharp极大函数以及分数次极大函数与BMO(R~n)函数生成的交换子在广义Morrey空间上有界性的等价刻画.     

Elliptic equations with BMO coefficients in Lipschitz domains

In this paper, we study inhomogeneous Dirichlet problems for elliptic equations in divergence form. Optimal regularity requirements on the coefficients and domains for the estimates are obtained. The principal coefficients are supposed to be in the John-Nirenberg space with small BMO semi-norms. The domain is supposed to have Lipschitz boundary with small Lipschitz constant. These conditions for the theory do not just weaken the requirements on the coefficients; they also lead to a more general geometric condition on the domain.

     

非线性Klein-Gordon方程整体解存在的最佳条件

本文研究一类带竞争势函数的非线性Klein-Gordon方程的柯西问题.根据基 态的特征,运用势井方法和凹方法导出了该问题解爆破和整体存在的最佳条件. 同时 还回答了当初值为多小时,整体解存在这个问题.     

Weighted Lp Estimates for Maximal Commutators of Multilinear Singular Integrals

This paper is concerned with the pointwise estimates for the sharp function of two kinds of maximal commutators of multilinear singular integral operators T∑b^＊ and TПb^＊ which are generalized by a weighted BMO function b and a multilinear singular integral operator T, respectively. As applications, some commutator theorems are established.     

The Conormal Derivative Problem for Elliptic Equations with BMO Coefficients on Reifenberg Flat Domains

We study the inhomogeneous conormal derivative problem for thedivergence form elliptic equation, assuming that the principalcoefficients belong to the BMO space with small BMO semi-normsand that the boundary is -Reifenberg flat. These conditionsfor the W^{1, p}-theory not only weaken the requirements on thecoefficients but also lead to a more general geometric conditionon the domain. In fact, the Reifenberg flatness is the minimalregularity condition for the W^{1, p}-theory. 2000 MathematicsSubject Classification 35R05 (primary), 35J15 (secondary).     

Schauder Estimates for Elliptic and Parabolic Equations

In this note the author gives an elementary and simple proof for the Schauder estimates for elliptic and parabolic equations. The proof also applies to nonlinear equations.