The mean curvature measure

Dai, Quiyi, Trudinger, Neil S., and Wang, Xu-Jia. "The mean curvature measure." Journal of the European Mathematical Society 014.3 (2012): 779-800. <http://eudml.org/doc/277659>.

@article{Dai2012,
abstract = {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.},
author = {Dai, Quiyi, Trudinger, Neil S., Wang, Xu-Jia},
journal = {Journal of the European Mathematical Society},
keywords = {mean curvature measure; Harnack inequality; weak continuity of mean curvature operator; weak solution; mean curvature measure; Harnack inequality; weak continuity of mean curvature operator; weak solution},
language = {eng},
number = {3},
pages = {779-800},
publisher = {European Mathematical Society Publishing House},
title = {The mean curvature measure},
url = {http://eudml.org/doc/277659},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Dai, Quiyi
AU - Trudinger, Neil S.
AU - Wang, Xu-Jia
TI - The mean curvature measure
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 3
SP - 779
EP - 800
AB - 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.
LA - eng
KW - mean curvature measure; Harnack inequality; weak continuity of mean curvature operator; weak solution; mean curvature measure; Harnack inequality; weak continuity of mean curvature operator; weak solution
UR - http://eudml.org/doc/277659
ER -