Abstract
We prove that for harmonic quasiconformal mappings α-Holder continuity on the boundary implies α-Holder continuity of the map itself. Our result holds for the class of uniformly perfect bounded domains, in fact we can allow that a portion of the boundary is thin in the sense of capacity. The problem for general bounded domains remains open.
Highlights
The following theorem is the main result in [1]
We prove that for harmonic quasiconformal mappings a-Hölder continuity on the boundary implies a-Hölder continuity of the map itself
Our result holds for the class of uniformly perfect bounded domains, we can allow that a portion of the boundary is thin in the sense of capacity
Summary
The following theorem is the main result in [1]. Theorem 1.1. Our result holds for the class of uniformly perfect bounded domains, we can allow that a portion of the boundary is thin in the sense of capacity. The following theorem is the main result in [1].
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