四元数分析中的T算子与两类边值问题

本文研究四元数分析中的非齐次 Ｄｉｒａｃ方程．引入了这类方程的分布解即 Ｔ算子,证明了Ｔ算子的一些性质并考察了非齐次Ｄｉｒａｃ方程的Ｄｉｒｉｃｈｌｅｔ边值问题,并将结果推广到高阶非齐次Ｄｉｒａｃ方程及这种方程的一类边值问题的情况．     

COMPLEX MONGE-AMPEREEQUATIONS ON GENERAL DOMAINS

Abstract. The smooth solutions of the Dirichlet problems for the complex Monge-Ampere equa-tions on general smooth domains are found ,provided that there exists a C3 strictly plurisub har-monic subsolution with prescribed boundary value. It is the smooth version of an existence theo-rem given by Bedford and Taylor.     

COMPLEX MONGE-AMPěRE EQUATIONS ON GENERAL DOMAINS

§ 1　 IntroductionThe complex Monge-Ampère equation is an important topic in the theory of severalcomplex variables,and has been intensively studied in last three decades.See[1 ] for thehistorical account and references therein.There are many results proved forstrongly pseu-doconvex domains.The complex Monge-Ampère equations in weakly pseudoconvex do-mains ornon-pseudoconvex domains are also interesting.For example,letΩ0 Ω1 be twostrongly pseudoconvex domains,an intrinsic norm of homo…     

二阶方程Dirichlet边值问题混合元的超收敛

我们考虑二阶方程Dirichlet边值问题混合元的超收敛。在正则矩形网格上,采用一阶Raviart-Thomas混合元空间,对有限元解经后处理后,其收敛于精确解的速度从二阶提高到四阶。     

实二次数域的 Kronecker 极限公式(Ⅲ)

讨论实二次数域的一类L-函数,证明了它的 Kronecker 极限公式. 这推广了E. Hecke 的一个结果,并由此得出某类实二次数域基本单位的一个有趣的恒等式.     

一类具有p-Laplacian的非线性特征值问题

利用变分法中的一个三临界点定理,在适当的假设下,研究了一类具有p-Laplacian的特征值Dirichlet问题至少存在三个弱解的充分条件.     

Deterministic homogenization of nonlinear degenerate elliptic operators with nonstandard growth

We study the deterministic homogenization of nonlinear degenerate elliptic equations with nonstandard growth.One fundamental in this topic is to extend the classical compactness results of theΣ-convergence method to the Orlicz spaces.We also show that one can homogenize nonlinear Dirichlet problems in a general way by leaning on a simple abstract hypothesis contrary to what has been done in the determinstic homogenization theory.     

一类Curvature方程的两种边值问题解的存在性

利用含有伪单调算子的变分不等式解的存在性定理,证明一类具有Dirichlet边值条件的Curvature方程在W1,p(Ω)空间中存在唯一解.深入研究具有Dirichlet边值条件的Curvature方程和具有Neumann边值条件的Curvature方程之间的关系,利用极大单调算子值域的扰动理论,给出具有Neumann边值条件的Curvature方程在W1,p(Ω)空间中存在解的充分条件.文中采用一些新的证明技巧,推广和补充了以往的相关研究成果.     

EXISTENCE OF THREE SOLUTIONS TO NONLINEAR DISCRETE DIRICHLET PROBLEM INVOLVING p-LAPLACIAN

In this paper, we study a nonlinear Dirichlet boundary value problem for difference equations involving the p-Laplacian with two positive parameters. One result on the existence of at least three solutions for this problem is obtained using critical point theory.     

圆环上Dirichlet空间中的Toeplitz算子及其代数性质

主要讨论了:(1)圆环上Dirichlet空间D~p(1P+∞),以φ∈L~(∞,1)为符号的Toeplitz算子T_φ的紧性等价条件-T_φ的Berezin变换在圆环的两边界上为0;(2)圆环上Dirichlet空间D~2,以u∈C~1(M)为符号的Toeplitz算子T_u的性质,并得到典型分解式:S=T_S+R,其中R为换位子,S=T_(uij).