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arXiv · 1912.06327

Nonnegative Whitney Extension Problem for $C^1(\mathbb{R}^n)$

Fushuai Jiang
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Abstract

Let $ f $ be a real-valued function on a compact subset in $ \mathbb{R}^n $. We show how to decide if $ f $ extends to a nonnegative and $ C^1 $ function on $ \mathbb{R}^n $. There has been no known result for nonnegative $ C^m $ extension from a general compact set $ E $ when $ m > 0 $. The nonnegative extension problem for $ m \geq 2 $ remains open.

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Fushuai Jiang. 2019-12-13. Nonnegative Whitney Extension Problem for $C^1(\mathbb{R}^n)$. https://arxiv.org/abs/1912.06327

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