Lower semicontinuity and existence results for anisotropic TV functionals with signed measure data
Analysis of PDEs
2026-01-29 v4
Abstract
We study the minimization of anisotropic total variation functionals with additional measure terms among functions of bounded variation subject to a Dirichlet boundary condition. More specifically, we identify and characterize certain isoperimetric conditions, which prove to be sharp assumptions on the signed measure data in connection with semicontinuity, existence, and relaxation results. Furthermore, we present a variety of examples which elucidate our assumptions and results.
Keywords
Cite
@article{arxiv.2404.07631,
title = {Lower semicontinuity and existence results for anisotropic TV functionals with signed measure data},
author = {Eleonora Ficola and Thomas Schmidt},
journal= {arXiv preprint arXiv:2404.07631},
year = {2026}
}