Stability and Continuity of Functions of Least Gradient

H. Hakkarainen; R. Korte; P. Lahti; N. Shanmugalingam

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 123-139, electronic only
  • ISSN: 2299-3274

Abstract

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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.

How to cite

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H. Hakkarainen, et al. "Stability and Continuity of Functions of Least Gradient." Analysis and Geometry in Metric Spaces 3.1 (2015): 123-139, electronic only. <http://eudml.org/doc/271003>.

@article{H2015,
abstract = {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.},
author = {H. Hakkarainen, R. Korte, P. Lahti, N. Shanmugalingam},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {least gradient; BV; metric measure spac; approximate continuity; continuity; stability; jump set; Dirichlet problem; minimal surface; BV; metric measure space},
language = {eng},
number = {1},
pages = {123-139, electronic only},
title = {Stability and Continuity of Functions of Least Gradient},
url = {http://eudml.org/doc/271003},
volume = {3},
year = {2015},
}

TY - JOUR
AU - H. Hakkarainen
AU - R. Korte
AU - P. Lahti
AU - N. Shanmugalingam
TI - Stability and Continuity of Functions of Least Gradient
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 123
EP - 139, electronic only
AB - 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.
LA - eng
KW - least gradient; BV; metric measure spac; approximate continuity; continuity; stability; jump set; Dirichlet problem; minimal surface; BV; metric measure space
UR - http://eudml.org/doc/271003
ER -

References

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