平面上边值问题的函数理论方法。I:光滑的情况

A. Soldatov
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引用次数: 14

摘要

考虑了阶平面上只含常系数前导项的椭圆系统的一般(不一定是局部)边值问题。利用一阶常三角矩阵椭圆系统的泛函理论方法,这个问题被简化为边界上的一个等价的泛函积分方程组。特别地,用这种方法得到了问题是诺埃尔问题的判据及其指标的计算公式。所有的考虑都是在光滑情况下进行的,即区域边界没有角点,而边界算子作用于连续函数空间。
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A FUNCTION THEORY METHOD IN BOUNDARY VALUE PROBLEMS IN THE PLANE. I: THE SMOOTH CASE
A general (not necessarily local) boundary value problem is considered for an elliptic system on the plane of th order containing only leading terms with constant coefficients. By a method of function theory developed for elliptic systems of first order with a constant triangular matrix , ; this problem is reduced to an equivalent system of integrofunctional equations on the boundary. In particular, a criterion that the problem be Noetherian and a formula for its index are obtained in this way. All considerations are carried out in the smooth case when the boundary of the domain has no corner points, while the boundary operators act in spaces of continuous functions.
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