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Energy Space Approaches to the Cauchy Problem for Poisson’s Equation

icon-email Phan Xuan Thanh , Olaf Steinbach

Abstract

Variational methods coupled with Tikhonov’s regularization for solving the Cauchy problem for Poisson’s equation are suggested and studied. The novel idea is to use the Tikhonov regularization term in H1/2 norm rather than in L2 norm. The penalty term is evaluated by some appropriate boundary integral operators. The optimality condition in the form of boundary integral equations is derived and then discretized by the Galerkin boundary element method. The error estimates for the discretized problems are proved for noisy data. Some numerical examples and comparisons with the L2 setting are presented for showing the efficiency of our approaches.

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
Lịch hoạt động chung Lịch sử dụng phòng, hội trường, hội thảo Ảnh hoạt động
Giới thiệu Đăng nhập Đăng ký tài khoản Quên mật khẩu Chính sách bảo mật
Messages2TimelineExceptionsViews8RouteQueries108Models432MailsGateSessionRequest
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      • 19. /app/Repositories/Pages/PagesRepository.php:108
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      • 19. /app/Repositories/Pages/PagesRepository.php:108
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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
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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
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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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