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CONDITIONS DE PROLONGEMENT HARMONIQUE ET SES APPLICATIONS

icon-email NGUYỄN THỪA HỢP

Abstract

Beaucoup de propriétés des fonctions analytiques se généralisent aux fonction harmoniques à n variables. Parmi eux, on a bien connu des propriétés classiques: l'analycité, le theorème de Liouville, le développement en série, etc...

Il est intéressant, dans le domaine des fonctions harmoniques, d'étudier des modèles analogues aux problèmes du saut, les problèmes de Riemann et de Hilbert etc... Relativement à ce sujet, les premiers résultats sur les problèmes du saut ont été obtenus dans [5], [6].

Dans la théorie des pròblèmes aux limites des fonctions analytiques, on sait bien l'importance des conditions de prolongement analytique d'une fonction donnée sur une courbe fermée à l'intérieur de cette courbe [3]. Dans le présent article, nous établissons les conditions analogues: celles de prolongement harmonique. Plus précisément, nous étudions les conditions nécessaires et suffisantes pour qu'il existe dans un domaine une fonction harmonique telle que les valeurs limites de cette fonction et de sa dérivée normale sur la frontière du domaine soient égales à des fonctions données.

À titre d'applications, nous étudions la résolution effective des diverses équations du potentiel et donnons la représentation intégrale d'une fonction harmonique dans un domaine multiplement connexe.

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
Messages2TimelineExceptionsViews8RouteQueries108Models431MailsGateSessionRequest
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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
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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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