Page 1

Displaying 1 – 3 of 3

Showing per page

Short-time heat flow and functions of bounded variation in R N

Michele Miranda, Diego Pallara, Fabio Paronetto, Marc Preunkert (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove a characterisation of sets with finite perimeter and B V functions in terms of the short time behaviour of the heat semigroup in R N . For sets with smooth boundary a more precise result is shown.

Stability and Continuity of Functions of Least Gradient

H. Hakkarainen, R. Korte, P. Lahti, N. Shanmugalingam (2015)

Analysis and Geometry in Metric Spaces

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.

Structural Properties of Solutions to Total Variation Regularization Problems

Wolfgang Ring (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In dimension one it is proved that the solution to a total variation-regularized least-squares problem is always a function which is "constant almost everywhere" , provided that the data are in a certain sense outside the range of the operator to be inverted. A similar, but weaker result is derived in dimension two.

Currently displaying 1 – 3 of 3

Page 1