<em>E</em><sub>2</sub>类二阶椭圆组一般形式的非线性边值问题

E₂类二阶椭圆组一般形式的非线性边值问题

基金项目: 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)

1.
Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China;
2.
Department of Computational Sciences, East China Institute of Technology, Fuzhou, Jiangxi 344000, P. R. China

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,证得了该问题的可解性.
- 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
Abstract: 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.
- elliptic systems /
- boundary value problems /
- singular integral equations /
- singular integral operators /
- existence

[1]	Wolfersdorf L V.A class of nonlinear Riemann-Hilbert problems for holomorphic functions[J].Math Nachr,1984,116(1):89-107.
[2]	Wolfersdorf L V.A class of nonlinear Riemann-Hilbert problems with monotone nonlinearity[J].Math Nachr,1987,130(1):111-119.
[3]	Kencht Sigrid,Mashimba Ali Seif.On the existence of a solution to the Riemann-Hilbetrt problems for a partial differential equation[J].Complex Variables,1986,6(2):240-263.
[4]	Gilbert R P,LI Ming-zhong.A class of nonlinear Riemann-Hilbert problems for the second order elliptic system[J].Complex Variables,1997,32(1):105-129.
[5]	LI Ming-zhong.Nonlinear boundary value problems for the first order elliptic system with the general form[A].In:CHIEN Wei-zang Ed.Proceedings of the Third International Conference on Nonlinear Mechanics[C].Shanghai:Shanghai University Press,1998,809-812.
[6]	李明忠,侯宗义,徐振远.椭圆型方程组理论和边值问题[M].上海:复旦大学出版社,1990,18-68.
[7]	Begehr H,Hsiao G C.On nonlinear boundary value problems for an elliptic system in the plane[A].In:Lecture Notes in Mathematics 846[C].Berlin:Springer-Verlag,1981,55-63.