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Advances in Pure and Applied Mathematics

Editor-in-Chief: Trimeche, Khalifa

Editorial Board: Aldroubi, Akram / Anker, Jean-Philippe / Aouadi, Saloua / Bahouri, Hajer / Baklouti, Ali / Bakry, Dominique / Baraket, Sami / Ben Abdelghani, Leila / Begehr, Heinrich / Beznea, Lucian / Bezzarga, Mounir / Bonami, Aline / Demailly, Jean-Pierre / Fleckinger, Jacqueline / Gallardo, Leonard / Ismail, Mourad / Jarboui, Noomen / Jouini, Elyes / Karoui, Abderrazek / Kamoun, Lotfi / Kobayashi, Toshiyuki / Maday, Yvon / Marzougui, Habib / Mili, Maher / Mustapha, Sami / Ovsienko, Valentin / Peigné, Marc / Pouzet, Maurice / Radulescu, Vicentiu / Schwartz, Lionel / Sifi, Mohamed / Zaag, Hatem / Zarati, Said

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CiteScore 2016: 0.36

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Source Normalized Impact per Paper (SNIP) 2016: 0.717

Mathematical Citation Quotient (MCQ) 2016: 0.28

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1869-6090
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Solutions to conjugate Beltrami equations and approximation in generalized Hardy spaces

Y. Fischer / J. Leblond
Published Online: 2010-05-07 | DOI: https://doi.org/10.1515/apam.2010.026

Abstract

We present a constructive method for the robust approximation to solutions of some elliptic equations in a plane domain from incomplete and corrupted boundary data. We state this inverse problem in generalized Hardy spaces of functions satisfying the conjugate Beltrami equation, of which we give some properties, in the Hilbertian framework. The issue is then reworded as a constrained approximation (bounded extremal) problem which is shown to be well-posed. A practical motivation comes from modelling plasma confinement in a tokamak reactor. There, the particular form of the conductivity coefficient leads to Bessel-exponential type families of solutions of which we establish density properties.

About the article

Received: 2009-12-04

Revised: 2010-03-12

Published Online: 2010-05-07

Published in Print: 2011-01-01


Citation Information: Advances in Pure and Applied Mathematics, Volume 2, Issue 1, Pages 47–63, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam.2010.026.

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[1]
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[2]
Isabelle Chalendar and Jonathan R. Partington
Complex Analysis and Operator Theory, 2016, Volume 10, Number 1, Page 61

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