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BOUNDARY VALUE PROBLEMS IN C AND Cn

icon-email HEINRICH BEGEHR

Abstract

Boundary value problems which are unconditionally solvable for one complex variable are in general not solvable for several complex variables. This phenomenon will be explained in the case of the Schwarz problem for polydiscs. Besides analytic functions, inhomogeneous Cauchy-Riemann systems are investigated. These systems in several complex variables are
overdetermined. Another overdetermined system in two complex variables is considered by introducing a proper hypercomplex variable and solved under Riemann-Hilbert boundary conditions on some submanifold of the boundary under consideration.
The theory of bianalytic functions is used to reduce the stress boundary value problem in orthotropic elasticity to boundary value problems for analytic functions in plane domains. This paper is the improved version of [17] in which formula (16) was incorrect. As for the Poisson equation (n=1) the solution should contain fundamental solutions (Green functions) in the kernels of the integrals.

Viện Toán học, Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Địa chỉ: Số 18 đường Hoàng Quốc Việt, quận Cầu Giấy, Hà Nội

Điện thoại: 024 37563474 - Fax: 024 37564303

Email: vientoan@math.ac.vn

Viện nghiên cứu cao cấp về toán Hội Toán học Mỹ MathScinet Thư viện số (VAST) Arxiv
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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      Metadata
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