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Analysis days in Sirius
October 26, 2021 15:00–15:45, Sochi, online via Zoom at 14:00 CEST (=13:00 BST, =08:00 EDT)
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Bianalytic functions of Hölder classes in Jordan domains with nonanalytic boundaries
M. Ya. Mazalov National Research University "Moscow Power Engineering Institute" in Smolensk
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Number of views: |
This page: | 155 |
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Abstract:
We consider some boundary behavior effect for bianalytic functions related to the Dirichlet problem solvability. There exist such Jordan domains (even with infinitely smooth but not analytic boundaries) where non-constant bianalytic functions can tend to zero near the boundary only sufficiently slow. More precisely, we prove that for any $\alpha$ and $\beta$ such that $0<\alpha<\beta<1$, there exists a Jordan domain $D=D(\alpha,\beta)$ in which there are nontrivial solutions of the homogeneous Dirichlet problem for the class ${\rm Lip_{\alpha}}(\overline{D})$. At that, every boundary arc is a uniqueness set for functions bianalytic in $D$ and belonging to the class ${\rm Lip_{\beta}}(\ovz{D})$.
Language: English
Website:
https://us02web.zoom.us/j/6250951776?pwd=aG5YNkJndWIxaGZoQlBxbWFOWHA3UT09
* ID: 625 095 1776, password: pade |
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