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arXiv · 1511.04804

Finiteness Principles for Smooth Selection

Charles Fefferman·Arie Israel·Garving K. Luli
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Abstract

In this paper we prove finiteness principles for $C^{m}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right) $-selection, and for $C^{m-1,1}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right) $-selection, in particular providing a proof for a conjecture of Brudyni-Shvartsman (1994) on Lipschitz selections for the case when the domain is $X = \mathbb{R}^n$. Our results raise the hope that one can start to understand constrained interpolation problems in which e.g. the interpolating function $F$ is required to be nonnegative everywhere.

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Charles Fefferman, Arie Israel, Garving K. Luli. 2015-11-16. Finiteness Principles for Smooth Selection. https://arxiv.org/abs/1511.04804

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