摘要
研究了E2类二阶椭圆型方程组相当广泛的一类非线性边值问题· 通过引进一种代换把它化为一类非线性广义Riemann＿Hilbert边值问题,再引进奇异积分算子,建立与该问题等价的非线性奇异积分方程· 应用奇异积分算子性质和泛函分析与函数论方法,在一定的假设条件下。
A class of nonlinear boundary value problems(BVP) for the second_order E2 class elliptic systems in general form is discussed. By introducing a kind of transformation,this kind of BVP is reduced to a class of generalized nonlinear Riemann_Hilbert BVP. And then some singular integral operators are introduced to establish the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of the properties of singular integral operators and the function theoretic methods.
出处
《应用数学和力学》
CSCD
北大核心
2003年第2期146-162,共17页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(19671056)
上海市自然科学基金资助项目(99ZA14030
01ZA14023)
江西省自然科学基金资助项目(981102
0211014)
关键词
椭圆型方程组
边值问题
奇异积分算子
奇异积分方程
存在性
elliptic systems
boundary value problems
singular integral equations
singular integral operators
existence
