Vector-valued optimal Lipschitz extensions
Name
Sheffield_Vector-valued optimal.pdf
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564.01 KB
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Adobe PDF
Checksum (MD5)
156ed56a2dd4768d6de56c17a5a663ce
Author(s)
Sheffield, Scott Roger
Smart, Charles
Date Issued
September 2011
Journal
Communications on Pure and Applied Mathematics
Publisher
Wiley Blackwell
Citation
Sheffield, Scott, and Charles K. Smart. “Vector-valued optimal Lipschitz extensions.” Communications on Pure and Applied Mathematics 65, no. 1 (January 28, 2012): 128-154.
Version
Original manuscript
Abstract
Consider a bounded open set U C R[superscript n] and a Lipschitz function g : aU → R[superscript 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.
Description
Original manuscript June 9, 2010
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1002/cpa.20391
