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The commutants of analytic Toeplitz operators for several complex variables

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Science China mathematics 2010年第7期53卷 1873-1880页

作者： Cao GuangFu Huang Sui guangzhou Univ Dept Math Guangzhou 510006 Guangdong Peoples R China

It is proved that if  is a nonconstant bounded analytic function on the unit ball B n and continuous on S n in C n , and ψ is a bounded measurable function on S n such that T * and T ψ commute, then ψ is the boundary value of an analytic function on B n . In addition, the commutants of two Toeplitz operators are also discussed.

关键词： Toeplitz operator commutant of an operator

PIECEWISE CONTINUOUS SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS IN THE PLANE

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Acta mathematica Scientia 1994年第4期14卷 384-392页

作者：戴道清 dept of math. Zhongshan University Guangzhou 510275 China

The Riemann boundary value problem is solved for the nonlinear elliptic equation in the plane W(z) = H(z, W, W(z)) + f(z,W). The function H is Lipschitz continuous with respect to the last two variables, with the Lipschitz constant for the last variable being strictly less than one (ellipticity condition). While the function f satisfies a natual growth condition with sigma > 0. \f(z,W)\ less-than-or-equal-to F(z)\W\sigma.

关键词：非线性椭园型方程分片连续解 Riemann边值问题

ON THE PERIODIC ORTHONORMAL WAVELET SYSTEM

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Acta mathematica Scientia 1998年第1期18卷 74-78页

作者：戴道清林伟 dept. of math. Zhongshan University Guangzhou 510275 China

This paper concerns with the point-wise convergence of a wavelet series for L-p functions and the characterization of Holder class by both the partial sums approximation and the best approximation.

关键词： wavelets periodic function partial sums the best approximation

MIXED BOUNDARY VALUE PROBLEM FOR SECOND－ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

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Acta mathematica Scientia 1995年第1期15卷 58-64页

作者：陈庆祥 dept. of math. Zhongshan University Guangzhou 510275 China

In this *** following ined boundary value problem for second-order system of differential equations of the elliptic type will be discussed to find the function u and v such that they satisfy:The solution of this problem is found by means of the theory of generalized analutic function and the integral equation method for solving boundary value problems.

关键词： elliptic type differential eguation boundary value problem

REGULARITY OF H^1 ∩L^(n((γ-1)/(2-γ))) WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS

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Acta mathematica Scientia 1990年第2期10卷 173-184页

作者：何旭东陈宝耀 dept. of math. Zhongshan Univ. Guangzhou China

Let us consider the following elliptic systems of second order-D_α(A_i~α(x, u, Du))=B_4(x, u, Du), i=1, …, N, x∈Q(?)R^n, n≥3 (1) and supposeⅰ) |A_i~α(x, u, Du)|≤L(1+|Du|);ⅱ) (1+|p|)^(-1)A_i~α(x, u, p)are H(?)lder-continuous functions with some exponent δ on (?)×R^N uniformly with respect to p, i.e.ⅲ) A_i~α(x, u, p) are differentiable function in p with bounded and continuous derivativesⅳ)ⅴ) for all u∈H_(loc)~1(Ω, R^N)∩L^(n(γ-1)/(2-γ))(Ω, R^N), B(x, u, Du)is ineasurable and |B(x, u, p)|≤a(|p|~γ+|u|~τ)+b(x), where 1+2/n0, b(x)∈L2n/(n+2), n^2/(n+2)+e(Ω), (?)ε>***. Only bounded open set Q will be considered in this paper; for all p≥1, λ≥0, which is clled a Morrey *** assumptions ⅰ)-ⅳ) hold, Giaquinta and Modica have proved the regularity of both the H^1 weak solutions of (1) under controllable growth condition |B|≤α(|p|~γ+|u|^((n+2)/(n-2))+b, 0<γ≤1+2/n and the H^1∩L~∞ weak solutions of (1) under natural growth condition |B|≤α|p|~2+b with a smallness condition 2aM<λ(|u|≤M), which implys that the H^1∩L~∞ weak solutions have the same regularty in the case of 1+2/n<γ<2. In the case of γ=2, many counterexamples (see [2] showed that u must be in H^1L~∞, while in the case of 1+2/n<γ<2, we consider the H^1∩L^n(γ-1)/(2-γ) weak solutions of (1), weaken the instability conditions upon them (from L~∞ to L^n(γ-1)/(2-γ) and obtain the same regularity results. Finally we show that the exponent n(γ-1)/(2-γ) can not be docreased anymore for the sake of the regularity *** 1. We call u∈H^1∩L^n(γ-1)/(2-γ)(Q, R^N) be a weak solution of (1), providod that where We use the convention that repeated indices are summed. i, j go from 1 to N ann α, β from 1 to n.

关键词： WEAK SOLUTIONS FOR NONLINEAR ELLIPTIC SYSTEMS REGULARITY OF H~1

THE CAUCHY TYPE INTEGRAL FOR M-ANALYTIC FUNCTION AND ITS APPLICATION

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Acta mathematica Scientia 1990年第2期10卷 149-166页

作者：林伟戴道清 dept. of math. Zhongshan Univ. Guangzhou China

In this paper, the Cauchy type integral for M-analytic function is investigated which is by definition the regular solution of the elliptic system f_x+Mf_y=0, where M is a constant m×m matrix without any real eigenva... 详细信息

关键词： Pr THE CAUCHY TYPE INTEGRAL FOR M-ANALYTIC FUNCTION AND ITS APPLICATION

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On λ-harmonic graphs

Applied mathematics(A Journal of Chinese Universities) 2009年第2期24卷 245-252页

作者： LIU Mu-huo LIU Bo-lian dept. of math. South China Agricultural Univ. Guangzhou 510642 China College of math. Sci. South China Normal Univ. Guangzhou 510631 China

A λ harmonic graph G, a λ-Hgraph G for short, means that there exists a constant A such that the equality λd（ui） = ∑（vi,vj）∈E（G） d（vj） holds for all i = 1, 2,…, ｜V（G）｜, where d（vi） denotes the degree of vertex vi. In this paper, some harmonic properties of the complement and line graph are given, and some algebraic properties for the λ-Hgraphs are obtained.

关键词： harmonic graph regular graph line graph degree series

NON-EXISTENCE FOR QUASILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS

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Acta mathematica Scientia 1992年第1期12卷 62-70页

作者：沈尧天马汝念 dept. of Appl. math. South China Univ. of Tech. Guangzhou 510641 China dept of math. Zhoungshan Univ. Guangzhou 510275 China

Since [1] established the Pohozaev identity in bounded domains, this identity has been the principal tool to deal with the non-existence of the equation

关键词： NON-EXISTENCE FOR QUASILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS ID

A　PHRAGMEN－LINDELOF　ALTERNATIVE　FOR　A　CLASS　OF　SECOND　ORDER　QUASILINEAR　EQUATIONS　IN　R^3

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Acta mathematica Scientia 1996年第2期16卷 181-191页

作者：林长好 dept. of math. South China Normal Univ. Guangzhou 510631 China

The present paper investigates the asymptotic behavior of solutions for a class of second order inhomogeneous quasilinear equations on a three dimensional semiinfinite cylinder. A Phragmen-Lindelof type alternative is obtained, i.e., it is shown that in appropriate norms solutions of the equations either grow or decay as some spatial variable tends to infinity.

关键词： quasilinear elliptic equation energy estimate Phragmen-Lindelof alternative.