Abstract
The limit equation of the p-Laplace equation as \(p\rightarrow \infty \) is a very fascinating one. In two variables it is the equation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For viscosity solutions some care is called for, see [HF].
- 2.
This result due to Grandall and Zhang has the consequence that the “mysterious inequality”
$$ \iiint \frac{|x-c|^2\langle x-a,x-b\rangle -\langle x-a,x-c\rangle \langle x-b, x-c\rangle }{|x-a||x-b||x-c|^3}\varrho (a)\varrho (b)\varrho (c)dadbdc\ge 0 $$has to hold for all compactly supported densities \(\varrho \).
- 3.
This is taken from my lecture notes in [L4].
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Lindqvist, P. (2019). The Infinity Laplacian. In: Notes on the Stationary p-Laplace Equation. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-14501-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-14501-9_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-14500-2
Online ISBN: 978-3-030-14501-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)