Regularity theory for elliptic and parabolic free boundary problems

椭圆和抛物线自由边界问题的正则理论

• 批准号: 417627993
• 负责人: Dr. Wenhui Shi, Ph.D.
• 金额: --
• 依托单位: School of Mathematics
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2019-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/417627993?language=en
• 关键词: Regularity; theory; elliptic; parabolic; free

The main objective of the proposal is to establish the regularity of solutions and free boundaries for free boundary problems. In particular, we focus on such problems which can be formulated as obstacle or Stefan type problems. Typically the problems we consider are evolutionary, or partially degenerate, or nonlocal, such that certain standard tools for the model problems are not available or hard to implement. We aim to develop new methods to treat the regularity and the long time asymptotics of solutions, and also to understand how degeneracy or nonlocal effects influence the behavior of the free boundaries.

该提案的主要目标是建立自由边界问题的解和自由边界的正则性。特别是，我们专注于这样的问题，可以制定为障碍或斯特凡型问题。通常，我们考虑的问题是进化的，或部分退化的，或非局部的，这样的模型问题的某些标准工具是不可用的或难以实现的。我们的目标是开发新的方法来处理的正则性和长时间渐近的解决方案，也了解如何退化或非局部效应影响的行为的自由边界。

项目成果

An epiperimetric inequality approach to the parabolic Signorini problem

抛物线 Signorini 问题的周长不等式方法

• DOI: 10.3934/dcds.2020095
• 发表时间: 2020
• 期刊: Discrete & Continuous Dynamical Systems - A
• 作者: Wenhui