JournalsrmiVol. 29, No. 4pp. 1405–1420

Defining functions for unbounded CmC^m domains

  • Phillip Harrington

    University of Arkansas, Fayetteville, USA
  • Andrew Raich

    University of Arkansas, Fayetteville, USA
Defining functions for unbounded $C^m$ domains cover
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Abstract

For a domain ΩRn\Omega\subset\mathbb{R}^n, we introduce the concept of a uniformly CmC^m defining function. We characterize uniformly CmC^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 CmC^m defining functions. Some of our results extend results from the bounded case.

Cite this article

Phillip Harrington, Andrew Raich, Defining functions for unbounded CmC^m domains. Rev. Mat. Iberoam. 29 (2013), no. 4, pp. 1405–1420

DOI 10.4171/RMI/762