Geodesic
The mean curvature measure
Journal of the European Mathematical Society, Tome 14 (2012) no. 3, pp. 779-800 Cet article a éte moissonné depuis la source EMS Press

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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 corresponding Dirichlet problem when the inhomogeneous term is a measure.
DOI : 10.4171/jems/318
Classification : 35-XX, 00-XX
Keywords: Mean curvature measure, Harnack inequality, weak continuity of mean curvature operator, weak solution 
@article{JEMS_2012_14_3_a5,
     author = {Qiuyi Dai and Neil S. Trudinger and Xu-Jia Wang},
     title = {The mean curvature measure},
     journal = {Journal of the European Mathematical Society},
     pages = {779--800},
     year = {2012},
     volume = {14},
     number = {3},
     doi = {10.4171/jems/318},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/318/}
}
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Qiuyi Dai; Neil S. Trudinger; Xu-Jia Wang. The mean curvature measure. Journal of the European Mathematical Society, Tome 14 (2012) no. 3, pp. 779-800. doi: 10.4171/jems/318

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