Uniqueness Theorems for Some Free Boundary Problems in Univalent Functions
Uniqueness Theorems for Some Free Boundary Problems in Univalent Functions
复制标题
一价函数中一些自由边界问题的唯一性定理
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
D. Tepper
中科院分区：
文献类型：
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作者：
Jonathan M. Huntey;N. Moh;D. Tepper
设Φ是复平面C上有界正连续函数。我们将考虑以下问题。我们可以找到一个包含原点的单连通区域Ω，使得单位圆盘D映射到Ω上的Riemann映射函数f Ω满足<artwork name="GCOV31013eu1">。我们证明了当Φ满足时，存在唯一解，该解关于原点是星形的。<artwork name="GCOV31013eu2">我们还证明了，如果另外，|W|>0且−log Φ是次调和的，则Ω将是凸区域。
Let Φ be a bounded positive continuous function in the complex plane C. We will consider the following problem. We can find a simply connected region Ω containing the origin such that the Riemann mapping function f Ω mapping the unit disk D onto Ω will satisfy <artwork name="GCOV31013eu1"> We show that there is a unique solution which is starlike with respect to the origin when Φ satisfies <artwork name="GCOV31013eu2"> We also show that if in addtion, ∂Φ/∂|w|>0 and −log Φ is subharmonic, then Ω will be a convex region.