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In this chapter, we study the boundary integro-differential equations of the boundary value problems of the Laplace equation. First, we recall some results on the boundary value problems of the Laplace equation. Then we discuss the potential theory corresponding to the Laplace equation. Finally, we reduce the boundary value problems of the Laplace equation to boundary integro-differential equations (or boundary integral equations).

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Boundary Value Problems of the Laplace Equation

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  • 发表日期：

    2026年

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  • Houde Han,
  • Dongsheng Yin

摘要

In this chapter, we study the boundary integro-differential equations of the boundary value problems of the Laplace equation. First, we recall some results on the boundary value problems of the Laplace equation. Then we discuss the potential theory corresponding to the Laplace equation. Finally, we reduce the boundary value problems of the Laplace equation to boundary integro-differential equations (or boundary integral equations).