Consider $\Omega_1, \Omega_2$ two convex, bounded domains in $R^n$ with $\Omega_1 \supset \overline{\Omega_2}$ suppose that $\operatorname{dist}(x, \partial \Omega_2) =\min_{y \in \partial \Omega_2} |x - y| = \lambda>0$ for all $x \in \partial \Omega_1$. Can I say anything about the regularity of $\partial \Omega_1$? I am asking this for curiosity. It seems that the regularity will be $C^1$. Someone could point me a reference please?
2026-04-08 16:16:52.1775665012
intuitive question about the boundary of a set
48 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ANALYSIS
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