The Beltrami equation
著者
書誌事項
The Beltrami equation
（Memoirs of the American Mathematical Society, no. 893）
American Mathematical Society, 2008
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注記
Bibliography: p. 89-92
内容説明・目次
内容説明
The ""measurable Riemann Mapping Theorem"" (or the existence theorem for quasiconformal mappings) has found a central role in a diverse variety of areas such as holomorphic dynamics, Teichmuller theory, low dimensional topology and geometry, and the planar theory of PDEs. Anticipating the needs of future researchers, the authors give an account of the ""state of the art"" as it pertains to this theorem, that is, to the existence and uniqueness theory of the planar Beltrami equation, and various properties of the solutions to this equation. The classical theory concerns itself with the uniformly elliptic case (quasiconformal mappings). Here the authors develop the theory in the more general framework of mappings of finite distortion and the associated degenerate elliptic equations.
目次
Introduction Quasiconformal mappings Partial differential equations Mappings of finite distortion Hardy spaces and BMO The principal solution Solutions for integrable distortion Some technical results Bibliography.
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