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THE MIXED PROBLEM FOR DEGENERATE ELLIPTIC EQUATIONS OF SECOND ORDER
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作者 Guochun Wen 《Analysis in Theory and Applications》 2005年第2期118-131,共14页
The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the e... The present paper deals with the mixed boundary value problem for elliptic equations with degenerate rank 0. We first give the formulation of the problem and estimates of solutions of the problem, and then prove the existence of solutions of the above problem for elliptic equations by the above estimates and the method of parameter extension. We use the complex method, namely first discuss the corresponding problem for degenerate elliptic complex equations of first order, afterwards discuss the above problem for degenerate elliptic equations of second order 展开更多
关键词 mixed problem elliptic equations degenerate rank 0
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The Riemann-Hilbert Problem for Mixed Complex Equations of First Order with Degenerate Rank 0 被引量:1
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作者 Guo-chun WEN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2015年第1期31-42,共12页
This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed (elliptic- hyperbolic) complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem an... This article deals with the Riemann-Hilbert boundary value problem for quasilinear mixed (elliptic- hyperbolic) complex equations of first order with degenerate rank 0. Firstly, we give the representation theorem and prove the uniqueness of solutions for the boundary value problem. Afterwards, by using the method of successive iteration, the existence and estimates of solutions for the boundary value problem are verified. The above problem possesses the important applications to the Tricomi problem of mixed type equations of second order. In this article, the proof of HSlder continuity of a singular double integer is very difficult and interesting as in this Section 4 below. 展开更多
关键词 Riemann-Hilbert problem quasilinear mixed complex equations degenerate rank 0 unique solv-ability of the problem HSlder continuity of singulax double integer
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退化秩为0的二阶混合型方程斜微商问题解的唯一性(英文) 被引量:3
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作者 闻国椿 《四川师范大学学报(自然科学版)》 CAS CSCD 2004年第2期115-123,共9页
讨论带抛物退化线的二阶混合型方程的斜微商边值问题,这个问题包括空气动力学中Chaplygin方程的Tricomi问题作为特殊情况.先给出这个问题的提法和解的表示式,然后使用复分析方法,证明了上述二阶混合型方程斜微商问题解的唯一性.
关键词 混合型方程 抛物退化线 斜微商问题的唯一性
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退化秩为0的二阶非线性混合型方程的Tricomi问题(英文)
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作者 闻国椿 杨丕文 《四川师范大学学报(自然科学版)》 CAS CSCD 北大核心 2009年第3期287-296,共10页
讨论退化秩为0的二阶非线性混合型方程的Tricomi问题,先给出这个问题的提法,得到了解的表示式,然后由逐次叠代的方法和列紧性原理证明这个问题解的存在性.
关键词 TRICOMI问题 非线性混合型方程 退化秩为0
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一阶拟线性退化椭圆型复方程的间断Riemann-Hilbert问题(英文)
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作者 闻国椿 杨丕文 《四川师范大学学报(自然科学版)》 CAS CSCD 北大核心 2007年第2期167-172,共6页
讨论退化秩为0的一阶拟线性椭圆型复方程的间断Riemann-Hilbert问题.先给出这个问题的提法和解的表示式,然后使用复分析方法证明了上述一阶椭圆型复方程Riemann-Hilbert解的存在性和唯一性.
关键词 间断Riemann—Hilbert边值问题 拟线性椭圆型复方程 退化秩为0
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