Abstract

We study solvability for a model elliptic pseudo-differential equation with an additional integral condition in Sobolev–Slobodetskii spaces in certain conical domains in Euclidean space. . Using the wave factorization for an elliptic symbol we construct a solution for this boundary value problem and study the behavior of the solution when parameters of cones tend to their extremal values. It was shown that for such a solvability we need certain additional condition besides presented integral condition.

中文翻译：

---

关于一些多维极限边值问题

摘要

我们研究了具有附加积分条件的模型椭圆伪微分方程的可解性，该方程在欧几里得空间的某些圆锥域中的 Sobolev-Slobodetskii 空间中。. 使用椭圆符号的波动分解，我们为这个边界值问题构建了一个解，并研究了当锥体的参数趋向于它们的极值时解的行为。结果表明，对于这样的可解性，除了提出的积分条件外，我们还需要某些附加条件。