Abstract

The paper is devoted to studying limit behavior for a solution of model elliptic pseudo-differential equation with some integral boundary condition in 4-wedge conical canonical 3D singular domain with two parameters. It is shown that the solution of such boundary value problem can have a limit with respect to endpoint values of the parameters in appropriate Sobolev–Slobodetskii space if the boundary function is a solution of a special functional singular integral equation.

中文翻译：

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关于某些三维极限边值问题

摘要

本文致力于研究带两个边界的4楔形圆锥规范3D奇异域中具有某些积分边界条件的模型椭圆型伪微分方程解的极限行为。结果表明，如果边界函数是一个特殊的奇异积分方程的解，那么这种边值问题的解就可以在适当的Sobolev–Slobodetskii空间中限制参数的端点值。