Abstract
Let be a domain, and suppose that for each a subset of is given. The problem is posed of finding conditions under which a function defined on the boundary can be extended to a -function defined in and such that the gradient satisfies . This problem is solved for the case when is a continuous distribution of bounded convex sets. An application is given to the description of the trace of a function with spacelike graph in a Lorentzian warped product. Bibliography: 10 titles.
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