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arXiv · 1111.4177

Defining Functions for Unbounded $C^m$ Domains

Phillip Harrington·Andrew Raich
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Abstract

For a domain $\Omega\subset\mathbb R^n$, we introduce the concept of a uniformly $C^m$ defining function. We characterize uniformly $C^m$ defining functions in terms of the signed distance function for the boundary and provide a large class of examples of unbounded domains with uniformly $C^m$ defining functions. Some of our results extend results from the bounded case.

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Phillip Harrington, Andrew Raich. 2011-11-17. Defining Functions for Unbounded $C^m$ Domains. https://arxiv.org/abs/1111.4177

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