How I met the normalized p-Laplacian $$\varDelta _p^N$$ and what we know now about mean values and concavity properties

Bernd Kawohl

Type: Article

Publication Date: 2020-03-23

Citations: 1

DOI: https://doi.org/10.1007/s41808-020-00060-2

Abstract

In this article I describe how I discovered the normalized p-Laplacian $$\varDelta _p^Nu=\frac{1}{p}|\nabla u|^{2-p}\varDelta _p u$$ as an interesting mathematical object in the context of mathematical image processing. Then I provide a survey of results which this operator has in common with the linear Laplacian.

Locations

Journal of Elliptic and Parabolic Equations - View - PDF

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Works Cited by This (36)

Action	Title	Year	Authors
+ PDF Chat	Rearrangements and Convexity of Level Sets in PDE	1985	Bernhard Kawohl
+ PDF Chat	First eigenvalue and maximum principle for fully nonlinear singular operators	2006	I. Birindelli Françoise Demengel
+ PDF Chat	On the Dirichlet and Serrin Problems for the Inhomogeneous Infinity Laplacian in Convex Domains: Regularity and Geometric Results	2015	Graziano Crasta Ilaria Fragalà
+	Maximum and comparison principle for one-dimensional anisotropic diffusion	1998	Bernd Kawohl Nikolai Kutev
+ PDF Chat	Tug-of-war with noise: A game-theoretic view of the p-Laplacian	2008	Yuval Peres Scott Sheffield⋆
+	Principal eigenvalue of a very badly degenerate operator and applications	2007	Petri Juutinen
+	Local behaviour of solutions to doubly nonlinear parabolic equations	2006	Juha Kinnunen Tuomo Kuusi
+	Remark on the preceding paper of Serrin	1971	Hans F. Weinberger
+	Positive eigenfunctions for the p-Laplace operator revisited	2006	Bernd Kawohl Peter Lindqvist
+	A deterministic‐control‐based approach motion by curvature	2005	Robert V. Kohn Sylvia Serfaty