Regularity of the One-phase Free Boundaries
Regularity of the One-phase Free Boundaries
复制标题
一相自由边界的正则性
DOI：
10.1007/978-3-031-13238-4
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
B. Velichkov
中科院分区：
文献类型：
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作者：
B. Velichkov
这本开放获取的书是对自由边界问题的正则性理论的介绍。本文的重点是单相Bernoulli问题，它对现代自由边界正则性理论的发展产生了深远的影响，至今仍是人们深入研究的对象。该论述围绕四个主要定理组织，它们以最简单的形式致力于单相泛函。这里介绍的许多方法和技术都是非常新的，是在不同的自由边界问题的背景下发展起来的。我们还给出了几个经典结果的详细证明，这些结果基于一些普遍的思想，在自由边界、偏微分方程组和几何正则性理论中是反复出现的。这本书是针对研究生和研究，任何人与中等水平的椭圆型偏微分方程组的知识。
This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research. The exposition is organized around four main theorems, which are dedicated to the one-phase functional in its simplest form. Many of the methods and the techniques presented here are very recent and were developed in the context of different free boundary problems. We also give the detailed proofs of several classical results, which are based on some universal ideas and are recurrent in the free boundary, PDE and the geometric regularity theories. This book is aimed at graduate students and researches and is accessible to anyone with a moderate level of knowledge of elliptical PDEs.