Existence theory for linear-growth variational integrals with signed measure data
Analysis of PDEs
2026-02-09 v3
Abstract
We develop a semicontinuity-based existence theory in for a general class of scalar linear-growth variational integrals with additional signed-measure terms. The results extend and refine previous considerations for anisotropic total variations and area-type cases, and they pave the way for a variational approach to the corresponding Euler-Lagrange equations, which involve the signed measure as right-hand-side datum.
Cite
@article{arxiv.2505.11279,
title = {Existence theory for linear-growth variational integrals with signed measure data},
author = {Eleonora Ficola and Thomas Schmidt},
journal= {arXiv preprint arXiv:2505.11279},
year = {2026}
}