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Russian Mathematical Surveys, 2010, Volume 65, Issue 1, Pages 1–94
DOI: https://doi.org/10.1070/RM2010v065n01ABEH004661 (Mi rm9341) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Functional geometric method for solving free boundary problems for harmonic functions

A. S. Demidovab

a M. V. Lomonosov Moscow State University
b Moscow Institute of Physics and Technology
English version PDF (1702 kB) Citations (15)
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DOI: https://doi.org/10.1070/RM2010v065n01ABEH004661
Abstract: A survey is given of results and approaches for a broad spectrum of free boundary problems for harmonic functions of two variables. The main results are obtained by the functional geometric method. The core of these methods is an interrelated analysis of the functional and geometric characteristics of the problems under consideration and of the corresponding non-linear Riemann–Hilbert problems. An extensive list of open questions is presented.
Bibliography: 124 titles.
Keywords: free boundaries, harmonic functions.
Received: 11.12.2009
Russian version:
Uspekhi Matematicheskikh Nauk, 2010, Volume 65, Issue 1(391), Pages 3–96
DOI: https://doi.org/10.4213/rm9341
Bibliographic databases:
Document Type: Article
UDC: 517.57
MSC: Primary 31A05, 35C20, 35R35, 35Q99, 76D27; Secondary 76W05, 82D10
Language: English
Original paper language: Russian
Citation: A. S. Demidov, “Functional geometric method for solving free boundary problems for harmonic functions”, Uspekhi Mat. Nauk, 65:1(391) (2010), 3–96; Russian Math. Surveys, 65:1 (2010), 1–94
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:109
    First page:66
     
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