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Potentials for Three-Dimensional Singular Elliptic Equation and Their Application to the Solving a Mixed Problem
Lobachevskii Journal of Mathematics Pub Date : 2020-07-18 , DOI: 10.1134/s1995080220060086 T. G. Ergashev
中文翻译:
三维奇异椭圆方程的势及其在求解混合问题中的应用
更新日期:2020-07-18
Lobachevskii Journal of Mathematics Pub Date : 2020-07-18 , DOI: 10.1134/s1995080220060086 T. G. Ergashev
Abstract
In earlier research, the double- and simple layer potentials have been successfully applied in solving boundary value problems for two-dimensional elliptic equations. Despite the fact that all fundamental solutions of a three-dimensional elliptic equation with one, two and three singular coefficients were known, the potential theory was not constructed in any case of a singularity. Here, in this paper, our goal is to construct a potential theory corresponding to the three-dimensional elliptic equation with one singular coefficient. We used some properties of Gaussian hypergeometric function to prove the limiting theorems, while deriving integral equations concerning the denseness of potentials.中文翻译:
三维奇异椭圆方程的势及其在求解混合问题中的应用