Dynamical approach to an overdetermined problem in potential theory
Dynamical approach to an overdetermined problem in potential theory
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势论中超定问题的动态方法
DOI：
10.1016/j.matpur.2016.03.011
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Michiaki Onodera
中科院分区：
文献类型：
--
作者：
Michiaki Onodera
我们介绍了一种新的方法来研究的唯一性和稳定性的一个域承认的超定问题的可解性。一个关键的观察是，变形的连续变化的域的参数化超定问题形成一个分析半流。这使我们能够获得一个域的唯一性，为原来的“固定”超定问题连同其形状的定量估计，通过澄清的动力学结构的半流。
We introduce a new approach for studying the uniqueness and stability of a domain admitting the solvability of an overdetermined problem. One of the key observations is that the deformation of a continuously varying domain for a parametrized overdetermined problem forms an analytic semiflow. This allows us to obtain the uniqueness of a domain for the original “stationary” overdetermined problem together with a quantitative estimate of its shape by clarifying the dynamical structure of the semiflow.