Defining functions for open sets in \(\mathbb R^n\). (English) Zbl 1108.26020

Burgués, J. M.

Real Anal. Exch. 31(2005-2006), No. 1, 45-53 (2006).

The author gives, for any given open subset \(\Omega\subset\mathbb{R}^n\), a function describing the boundary of this set with exact regularity end being, globally, as regular as possible. By means of this function it is possible to obtain a family of smooth domains whose boundaries approximate \(\partial\Omega\) in a controlled way.

Reviewer: Octavian Lipovan (Timişoara)

MSC:

26E99	Miscellaneous topics in real functions
58C05	Real-valued functions on manifolds

Keywords:

differentiable function; non-regular