.png){kind=icon}
.png){kind=icon}
Return
Vector-Valued Optimal Lipschitz Extensions
.png){kind=icon}
OA
AI
DOI：10.1002/cpa.20391.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Consider a bounded open set U subset of R(n) and a Lipschitz function g : partial derivative U -> 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. (C) 2011 Wiley Periodicals, Inc.
Keywords:
SPACES
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
2.7
Papers:
1.5K
Citations:
1.1W
