How I met the normalized p-Laplacian Delta(N)(p) and what we know now about mean values and concavity properties

摘要

In this article I describe how I discovered the normalized p-Laplacian Delta pNu=1p| backward difference u|2-p Delta puas 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.