Vector‐valued optimal Lipschitz extensions
By Scott Sheffield, Charles K. Smart. 2010
65 citations recorded by the source corpus.
Consider a bounded open set $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}U \subset \R^n$ and a Lipschitz function $\font\open=msbm10 at 10pt\def\R{\hbox{\open R}}g: \partial U \to \R^m$. Does this function always have a canonical optimal Lipschitz extension to all of U? We propose a notion of optimal Lipschitz extension and address existence and uniqueness in some special cases. In the case n = m = 2, we show that smooth solutions have two phases: in one they are conformal and in the other they are variants of infinity harmonic functions called infinity harmonic fans. We also prove existence and uniqueness for the extension problem on finite graphs. © 2011 Wiley Periodicals, Inc.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/3f340b2b9e2f0ae1912d1cf299cdd7147830e533
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- On the Structure of ∞-Harmonic Maps (2014, methodology): “Sheffield and Smart in [29] used the nonsmooth operator norm on N×n as their Hamiltonian and derived a very singular variant of (1.”