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The mean curvature measure

Dai, Qiuyi; Trudinger, Neil; Wang, Xu-Jia

Description

We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions to the...[Show more]

CollectionsANU Research Publications
Date published: 2012
Type: Journal article
URI: http://hdl.handle.net/1885/62243
Source: European Mathematical Society Journal
DOI: 10.4171/JEMS/318

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