Communications in Mathematical Sciences
Volume 15 (2017)
Compact support of $L^1$ penalized variational problems
Pages: 1771 – 1790
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
Paper received on 10 October 2016.