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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 3, 2002, pp. 719–752
DOI: 10.4171/ZAA/1105

Published online: 2002-09-30

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

E.G. Grigoryeva[1], A.A. Klyachin[2] and V.M. Miklyukov[3]

(1) Volgograd State University, Russian Federation
(2) Volgograd State University, Russian Federation
(3) Volgograd State University, Russian Federation

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

Keywords: Lipschitz function, pseudometric, Finsler space, Minkowski space, space-like surface

Grigoryeva E.G., Klyachin A.A., Miklyukov V.M.: Problem of Functional Extension and Space-Like Surfaces in Minkowski Space. Z. Anal. Anwend. 21 (2002), 719-752. doi: 10.4171/ZAA/1105