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<p>A model elliptic pseudo-differential equation is considered in a plane with cuts along coordinate axes. Using special wave factorization for an elliptic symbol one can describe the kernel of the pseudo-differential equation in Sobolev–Slobodetskii space. To annihilate the kernel they use some boundary conditions on cuts sides. A unique solvability for obtained boundary value problem is reduced to the unique solvability for a system of certain linear integral equations.</p>

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On a Certain Boundary Value Problem in a Plane Excluding Axes

  • 期刊论文

  • 发表日期：

    2025年7月30日

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  • Vladimir Vasilyev,
  • Alexander Vasilyev,
  • Nataliya Agarkova

摘要

A model elliptic pseudo-differential equation is considered in a plane with cuts along coordinate axes. Using special wave factorization for an elliptic symbol one can describe the kernel of the pseudo-differential equation in Sobolev–Slobodetskii space. To annihilate the kernel they use some boundary conditions on cuts sides. A unique solvability for obtained boundary value problem is reduced to the unique solvability for a system of certain linear integral equations.