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Stability and continuity of functions of least gradient

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 نشر من قبل Nageswari Shanmugalingam
 تاريخ النشر 2014
  مجال البحث
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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.



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