Communications in Mathematical Sciences

Volume 15 (2017)

Number 6

Compact support of $L^1$ penalized variational problems

Pages: 1771 – 1790

DOI: http://dx.doi.org/10.4310/CMS.2017.v15.n6.a13

Authors

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

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

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

35A15

Full Text (PDF format)

Paper received on 10 October 2016.