广义Cauchy-Riemann系统的Dirichlet问题

Complex Variables, Theory and Application: An International Journal Pub Date : 2005-06-10 DOI:10.1080/02781070500087196

M. Reissig, A. Timofeev

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引用次数: 7

摘要

本文致力于在∂，Im w = h in z 0 = 1的单位磁盘G中的Dirichlet问题，其中G是一个给定的Hölder连续函数。系数b属于l2 (G)的一个子空间，一般不包含在Lq(G)中，q > 2。因此，Vekua的理论并不适用。然而，我们能够证明连续解的唯一性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Dirichlet problems for generalized Cauchy–Riemann systems with singular coefficients

The article is devoted to the Dirichlet problem in the unit disk G for on ∂, Im w = h in z 0 = 1, where g is a given Hölder continuous function. The coefficient b belongs to a subspace of L 2(G) which is in general not contained in Lq(G), q > 2. Thus Vekua's theory is not applicable. Nevertheless we are able to prove the uniqueness of continuous solutions in .

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Complex Variables, Theory and Application: An International Journal

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