Communications in Mathematical Sciences

Volume 15 (2017)

Number 6

Compact support of $L^1$ penalized variational problems

Pages: 1771 – 1790



Jonathan Siegel (Department of Mathematics, University of California at Los Angeles)

Omer Tekin (Department of Mathematics, University of California at Los Angeles)


We investigate the solutions to $L^1$ constrained variational problems. In particular, we are interested in the case where the $L^1$ term is weighted by some non-negative function. Extending previous results of Brezis et al, we prove that for a wide range of variational problems, the solutions have compact support. Additionally, we provide the results of some numerical experiments, where we computed the solutions to $L^1$ constrained elliptic and parabolic problems using splitting and ADMM.


$L^1$ regularization, variational methods, elliptic and parabolic PDE

2010 Mathematics Subject Classification


The full text of this article is unavailable through your IP address:

Received 10 October 2016

Published 27 June 2017