Revista Matemática Iberoamericana

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Volume 29, Issue 4, 2013, pp. 1405–1420
DOI: 10.4171/RMI/762

Published online: 2013-12-15

Defining functions for unbounded $C^m$ domains

Phillip Harrington[1] and Andrew Raich[2]

(1) University of Arkansas, Fayetteville, USA
(2) University of Arkansas, Fayetteville, USA

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.

Keywords: Defining function, signed distance function, unbounded domains, uniformly $C^m$ defining function

Harrington Phillip, Raich Andrew: Defining functions for unbounded $C^m$ domains. Rev. Mat. Iberoam. 29 (2013), 1405-1420. doi: 10.4171/RMI/762