JournalszaaVol. 21, No. 3pp. 719–752

Problem of Functional Extension and Space-Like Surfaces in Minkowski Space

  • E.G. Grigoryeva

    Volgograd State University, Russian Federation
  • A.A. Klyachin

    Volgograd State University, Russian Federation
  • V.M. Miklyukov

    Volgograd State University, Russian Federation
Problem of Functional Extension and Space-Like Surfaces in Minkowski Space cover
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Abstract

Let Ξ(x)\Xi (x) be the distribution of convex sets over a domain DRnD \subset \mathbb R^n and let ϕ:DR\phi: \partial D \rightarrow \mathbb R be a function. We consider the existence problem of locally Lipschitz functions ff defined in the domain DD so that fD=ϕf|_{\partial D} = \phi and f(x)Ξ(x)\bigtriangledown f (x) \in \Xi (x) almost everywhere in DD. These questions are related to the existence problem for space-like surfaces of arbitrary codimension with prescribed boundary in Minkowski space.

Cite this article

E.G. Grigoryeva, A.A. Klyachin, V.M. Miklyukov, Problem of Functional Extension and Space-Like Surfaces in Minkowski Space. Z. Anal. Anwend. 21 (2002), no. 3, pp. 719–752

DOI 10.4171/ZAA/1105