2019/04/07 by Shangbin Cui, Cui, Shangbin
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #math.AP
paper · pdf · doi:10.48550/arxiv.1904.04246
This is a revised version of a submission with the same title to the journal "Acta Applicandae Mathematicae" on November 1, 2018. arXiv admin note: text overlap with arXiv:1606.09393
arxiv created 2019/04/07 · openalex publication_date 2019/04/07 · arxiv updated 2019/04/10 · openalex created_date 2019/04/25 · openalex updated_date 2026/07/28
In this paper we study the Banach manifold made up of simple Cm+μ-domains in the Euclidean space ℝ. This manifold is merely a topological or a C0 Banach manifold. It does not possess a differentiable structure. We introduce the concept of differentiable point in this manifold and prove that it is still possible to introduce the concept of tangent vector and tangent space at a differentiable point. Consequent, it is possible to consider differential equations in this Banach space. We show how to reduce some important free boundary problems into differential equations in such a manifold and then use the abstract result that we established earlier to study these free boundary problems.