Riikka Korte

Stability and continuity of functions of least gradient

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.

Characterizations for the Hardy inequality

Necessary and sufficient conditions for the validity of a multidimensional version of the Hardy inequality are discussed. A characterization through a boundary Poincare inequality is considered.

The higher integrability of weak solutions of porous medium systems

Abstract In this paper we establish that the gradient of weak solutions to porous medium-type systems admits the self-improving property of higher integrability.

A characterization of {{\mathrm{BMO}}} self-maps of a metric measure space

This paper studies functions of bounded mean oscillation (

Homeomorphisms of the Heisenberg group preserving BMO

{{\mathrm{BMO}}}

Lebesgue points and capacities via the boxing inequality in metric spaces

BMO) on metric spaces equipped with a doubling measure. The main result gives characterizations for mappings that preserve

A connection between a general class of superparabolic functions and supersolutions

{{\mathrm{BMO}}}