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Abstract <p> A model pseudo-differential equation in a Sobolev–Slobodetskii space is considered ina cone which is a direct product of low-dimensional cones. Under the existence of a specialfactorization for the symbol, a general solution can be written, it includes arbitrary functions froma certain Sobolev–Slobodetskii space. A certain example in a three-dimensional space isconsidered, the unknown functions can be determined with help of Dirichlet conditions on a pieceof the boundary by reducing to a system of linear integral equations.</p>

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On Elliptic Problems and Integral Equations

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • A. V. Vasil’ev,
  • V. B. Vasil’ev,
  • I. O. Shmal

摘要

Abstract

A model pseudo-differential equation in a Sobolev–Slobodetskii space is considered ina cone which is a direct product of low-dimensional cones. Under the existence of a specialfactorization for the symbol, a general solution can be written, it includes arbitrary functions froma certain Sobolev–Slobodetskii space. A certain example in a three-dimensional space isconsidered, the unknown functions can be determined with help of Dirichlet conditions on a pieceof the boundary by reducing to a system of linear integral equations.