多维锥体中的伪微分方程和边值问题

Pub Date : 2024-02-26 DOI:10.1134/s0012266123120091

V. B. Vasil’ev

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引用次数: 0

摘要

摘要我们考虑了多维锥体中椭圆伪微分方程在 Sobolev-Slobodetskii 空间中的一个特殊边界值问题。考虑到椭圆符号的特殊因式分解，我们写出了包含任意函数的伪微分方程的一般解。为了明确地确定它，在方程中加入了一些积分条件，这使得用傅里叶变换写出解成为可能。

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Pseudodifferential Equations and Boundary Value Problems in a Multidimensional Cone

Abstract

We consider a special boundary value problem in the Sobolev–Slobodetskii space for a model elliptic pseudodifferential equation in a multidimensional cone. Taking into account the special factorization of the elliptic symbol, we write the general solution of the pseudodifferential equation that contains an arbitrary function. To determine it unambiguously, some integral condition is added to the equation, which makes it possible to write the solution in Fourier transforms.

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