(Quasi-)conformal methods in two-dimensional free boundary problems
(Quasi-)conformal methods in two-dimensional free boundary problems
复制标题
二维自由边界问题中的（拟）共形方法
DOI：
10.4171/jems/1435
复制
发表时间：
2021
影响因子：
2.6
通讯作者：
B. Velichkov
中科院分区：
文献类型：
--
作者：
G. Philippis;L. Spolaor;B. Velichkov
本文研究了几类自由边值问题解的局部性态。我们与准共形映射的理论的非线性薄障碍问题的解决方案的正则性，我们证明了接触集是局部的一个有限的区间并将此结果应用到解决方案的一相伯努利问题的几何约束。我们还介绍了一种新的共形速端图变换，它允许获得精确的扩展在分支点的解决方案的一个阶段的问题与几何约束和一类对称的解决方案的两相问题，以及构造自由边界的例子与尖状奇点。
In this paper we study the local behavior of solutions to some free boundary problems. We relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear thin-obstacle problems; we prove that the contact set is locally a finite union of intervals and we apply this result to the solutions of one-phase Bernoulli problems with geometric constraint. We also introduce a new conformal hodograph transform, which allows to obtain the precise expansion at branch points of both the solutions to the one-phase problem with geometric constraint and a class of symmetric solutions to the two-phase problem, as well as to construct examples of free boundaries with cusp-like singularities.
影响因子：
3.1
作者：
De Philippis, Guido;Spolaor, Luca;Velichkov, Bozhidar
通讯作者：
Velichkov, Bozhidar