Problem of functional extension and space-like surfaces in Minkowski space
type: Item
instance of: scholarly article
title: Problem of functional extension and space-like surfaces in Minkowski space
zbMATH Open document ID: 1021.53014
DOI: 10.4171/ZAA/1105
author: A. A. Klyachin
author: E. G. Grigor'eva
author: V. M. Miklyukov
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2003-01-21T00:00:00Z
review text: Let \(\Theta\) be a distribution of convex sets over a domain \(D \subset \mathbb{R}^n\) and \(\Phi : \partial D \rightarrow \mathbb{R}\) be a function. The authors consider the problem of the existence of locally Lipschitz functions \(f : D \rightarrow \mathbb{R}\) such that \(f|_{\partial D}= \Phi\) and \(\nabla f(x) \in \Theta (x)\) almost everywhere in \(D\). A criterion for the solvability of this problem is given, in the case of locally bounded convex sets in \(\Theta\). The results are applied to the existence problem of \(k\)-dimensional spacelike surfaces with prescribed boundary in the Minkowski space and in some warped Lorentzian products.
reviewed by: Gabriel Teodor Pripoae
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 1827608
zbMATH Keywords: functional extension problem
zbMATH Keywords: spacelike surface
zbMATH Keywords: Minkowski space
MaRDI profile type: Publication
cites work: Spacelike hypersurfaces with prescribed boundary values and mean curvature
cites work: Q5565773
cites work: Q3362952
description: scientific article; zbMATH DE number 1827608