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JOURNALS // Uspekhi Matematicheskikh Nauk // Archive

Uspekhi Mat. Nauk, 2010 Volume 65, Issue 1(391), Pages 3–96 (Mi rm9341)

This article is cited in 16 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

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.

UDC: 517.57

MSC: Primary 31A05, 35C20, 35R35, 35Q99, 76D27; Secondary 76W05, 82D10

Received: 11.12.2009

DOI: 10.4213/rm9341


 English version:
Russian Mathematical Surveys, 2010, 65:1, 1–94

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© Steklov Math. Inst. of RAS, 2026