E_2类二阶椭圆组一般形式的非线性边值问题  

A Class of Nonlinear Boundary Value Problems for the Sceond-Order E_2 Class Elliptic Systems in General Form

作　　者：李明忠[1] 徐定华[1] 

机构地区：[1]上海大学数学系,上海200436

出　　处：《应用数学和力学》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)

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 E2 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.

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 

分 类 号：O175.25[理学—数学] O175.8[理学—基础数学]