Let be the distribution of convex sets over a domain and let be a function. We consider the existence problem of locally Lipschitz functions defined in the domain so that and almost everywhere in . These questions are related to the existence problem for space-like surfaces of arbitrary codimension with prescribed boundary in Minkowski space.
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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. 719–752DOI 10.4171/ZAA/1105