Analysis of extended boundary-domain integral and integro-differential equations of some variable-coefficient BVP
Analysis of extended boundary-domain integral and integro-differential equations of some variable-coefficient BVP
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某些变系数BVP的扩展边域积分和积分微分方程分析
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发表时间：
2005
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通讯作者：
S. Mikhailov
中科院分区：
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作者：
S. Mikhailov
对于来自Sobolev空间H（Ω）的函数，考虑了非唯一外部和唯一内部协正规导数的定义，这些定义与偏微分算子及其右侧从指定的域Ω扩展到不指定的域边界的可能扩展有关。然后将这些概念应用于基于特殊构造的参数矩阵的直接边域积分和积分微分方程（BDIEs和BDIDEs）的公式和分析，并与具有变系数和相当一般的右侧的“拉普拉斯”线性微分方程的Dirichlet边值问题相关联。BDI(D) e包含定义在考虑域中并作用于未知解的势型积分算子，以及定义在边界上并作用于未知解的迹和/或协正规导数或辅助函数的积分算子。在适当的Sobolev空间中，研究了bdie /BDIDEs/ bdidp与原BVP的可解性、解唯一性和等价性。
For a function from the Sobolev space H(Ω) definitions of non-unique external and unique internal co-normal derivatives are considered, which are related to possible extensions of a partial differential operator and its right hand side from the domain Ω, where they are prescribed, to the domain boundary, where they are not. The notions are then applied to formulation and analysis of direct boundary-domain integral and integro-differential equations (BDIEs and BDIDEs) based on a specially constructed parametrix and associated with the Dirichlet boundary value problems for the ”Laplace” linear differential equation with a variable coefficient and a rather general right hand side. The BDI(D)Es contain potential-type integral operators defined on the domain under consideration and acting on the unknown solution, as well as integral operators defined on the boundary and acting on the trace and/or co-normal derivative of the unknown solution or on an auxiliary function. Solvability, solution uniqueness, and equivalence of the BDIEs/BDIDEs/BDIDPs to the original BVP are investigated in appropriate Sobolev spaces.