论文标题
强烈椭圆运算符的外部扩展问题：使用基本解决方案的溶解度和近似
Exterior extension problems for strongly elliptic operators: solvability and approximation using fundamental solutions
论文作者
论文摘要
在这项工作中，我们研究了强烈椭圆形方程的三个外部扩展问题：库奇问题（在特殊陈述中），“分析”延续问题和所谓的“内部” dirichlet问题，在sobolev空间的范围内，在域上具有相对平稳的边界。我们考虑了解决这些问题的解决方案，对于各种椭圆形的系统，这些问题的密集性解决性和条件良好。我们还通过单层电位和“离散”基本解决方案的线性组合来考虑解决这些问题的近似值，这与第二阶的较窄类别的较窄类别有关。获得的结果证明了边界积分方程的间接方法的适用性以及用于解决外部扩展问题的数值解决方案。
In this work we study three exterior extension problems for strongly elliptic partial equations: the Cauchy problem (in a special statement), the "analytical" continuation problem and the so called "inner" Dirichlet problem in the scale of the Sobolev spaces over a domain with relatively smooth boundaries. We consider the existence of solutions to these problems, the dense solvability and conditional well-posedness of these problems for a wide class of strongly elliptic systems. We also consider the approximation of solutions to these problems by a single layer potential and by a linear combination of "discrete" fundamental solutions in relation to a narrower class of strongly elliptic operators of the second order. The obtained results justify the applicability of the indirect method of boundary integral equations and for numerical solving the exterior extension problems.
