I did my doctoral studies at Aalto University and I collaborate mainly with members of
the Nonlinear PDE Research Group.
- Analysis on metric measure spaces
- Functions of bounded variation (BV functions)
- Fine potential theory for p=1
- Lower semicontinuity of functionals of linear growth
Recently I have mostly worked on extending results of fine potential theory from the case p>1 to the case p=1.
Such results in the case p=1 seem to be mostly new even in Euclidean spaces, but it is natural to study them in the more general setting of a metric space
equipped with a doubling measure and supporting a Poincaré inequality.
I am also interested in minimization problems and approximation results involving the BV class.