Geodesic
Stability and Continuity of Functions of Least Gradient
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.
Mots-clés : least gradient, BV; metric measure spac, approximate continuity, continuity, stability, jump set, Dirichlet problem, minimal surface 
@article{AGMS_2015_3_1_a15,
     author = {Hakkarainen, H. and Korte, R. and Lahti, P. and Shanmugalingam, N.},
     title = {Stability and {Continuity} of {Functions} of {Least} {Gradient}},
     journal = {Analysis and Geometry in Metric Spaces},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2015},
     zbl = {1318.26028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a15/}
}
TY  - JOUR
AU  - Hakkarainen, H.
AU  - Korte, R.
AU  - Lahti, P.
AU  - Shanmugalingam, N.
TI  - Stability and Continuity of Functions of Least Gradient
JO  - Analysis and Geometry in Metric Spaces
PY  - 2015
VL  - 3
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a15/
LA  - en
ID  - AGMS_2015_3_1_a15
ER  - 
%0 Journal Article
%A Hakkarainen, H.
%A Korte, R.
%A Lahti, P.
%A Shanmugalingam, N.
%T Stability and Continuity of Functions of Least Gradient
%J Analysis and Geometry in Metric Spaces
%D 2015
%V 3
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a15/
%G en
%F AGMS_2015_3_1_a15
Hakkarainen, H.; Korte, R.; Lahti, P.; Shanmugalingam, N. Stability and Continuity of Functions of Least Gradient. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a15/