Generalized implicit function theorems and problems with a free boundary
type: Item
instance of: scholarly article
title: Generalized implicit function theorems and problems with a free boundary
zbMATH Open document ID: 0860.35001
DOI: 10.1007/BF02367274
author: A. K. Kerimov
published in: Journal of Mathematical Sciences (New York)
publication date: 1997-04-21T00:00:00Z
review text: The content of the present work is as follows: In Sec. 1.1 the properties of superposition operators on Hölder classes are considered. Information on the derivatives along vector fields is presented in Sec. 1.2. Questions concerning perturbations of boundary value problems are considered in Sec. 1.3. The results of this section play a central role in the verification of assumptions of the generalized implicit function theorems. In Sec. 1.4 the parametrization of doubly-connected domains by functions defined on a definite manifold are considered. Local and global generalized implicit function theorems are presented in Chapter 2. In Sec. 2.1. the local existence, uniqueness and differentiability of the implicit function are considered. In Sec. 2.2 global variants of the generalized implicit function theorems are presented. In Chapter 3 and 4 classical problems are considered in view of the results of Chapter 1 and 2. Here we have conditions of global stability of these problems in Hölder classes together with data-dependence results in the dimension \(n\geq 2\). Finally, Chapter 4 is devoted to problems with Bernoulli's conditions on a free boundary.
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 26B10
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35B20
Mathematics Subject Classification ID: 49-02
zbMATH DE Number: 877644
zbMATH Keywords: local and global generalized implicit function theorems
zbMATH Keywords: superposition operators on Hölder classes
zbMATH Keywords: derivatives
zbMATH Keywords: perturbations of boundary value problems
zbMATH Keywords: generalized implicit function theorems
zbMATH Keywords: parametrization of doubly-connected domains
zbMATH Keywords: local existence, uniqueness and differentiability of the implicit function
zbMATH Keywords: global stability
zbMATH Keywords: data-dependence results
zbMATH Keywords: Bernoulli's conditions on a free boundary
reviewed by: Stefan Balint
MaRDI profile type: Publication
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