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Abstract <p> The solvability of a model elliptic pseudodifferential equation in canonical domains thatare products of cones is studied. A special factorization of the elliptic symbol is used to writea general solution of the equation in a Sobolev–Slobodetskii space. In the case under study, thissolution contains a pair of arbitrary functions. To determine these functions uniquely, someintegral conditions are added to the equation. The behavior of the solution is considered as someof the cone parameters approach their limit values.</p>

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On Model Pseudodifferential Equations in a Multidimensional Space

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • V. B. Vasil’ev,
  • H. F. Gebreslasie,
  • O. V. Chernova

摘要

Abstract

The solvability of a model elliptic pseudodifferential equation in canonical domains thatare products of cones is studied. A special factorization of the elliptic symbol is used to writea general solution of the equation in a Sobolev–Slobodetskii space. In the case under study, thissolution contains a pair of arbitrary functions. To determine these functions uniquely, someintegral conditions are added to the equation. The behavior of the solution is considered as someof the cone parameters approach their limit values.