Regularity of the distance function to the boundary
By Yanyan Li, L. Nirenberg. 2005
68 citations recorded by the source corpus.
Let $\Omega$ be a domain in a smooth complete Finsler manifold, and let $G$ be the largest open subset of $\Omega$ such that for every $x$ in $G$ there is a unique closest point from $\partial \Omega$ to $x$ (measured in the Finsler metric). We prove that the distance function from $\partial \Omega$ is in $C^{k,\alpha}_{loc}(G\cup \partial \Omega)$, $k\ge 2$ and $0<\alpha\le 1$, if $\partial \Omega$ is in $C^{k,\alpha}$.
View Paper: https://www.semanticscholar.org/paper/6525874518678f01384705f9fb95593726b231f6
How researchers see this paper
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- R. Lewis
- Junfang Li
- M. Dajczer
- P. A. Hinojosa
- J. H. Lira
- Yanyan Li
- Tianling Jin
- Luis Caffarelli
Citations in the corpus
- Killing graphs with prescribed mean curvature (2006, background): “It was shown in [ 8 ] that the function d in � 0 has the same regularity as � .”
- A geometric characterization of a sharp Hardy inequality (2011, background): “Note that a proof of this result in the much more general setting of Finsler manifolds was given in [27, 28].”