Published Paper

Inserted: 16 may 2025
Last Updated: 5 feb 2026

Journal: Adv. Calc. Var.
Volume: 19
Number: 1
Pages: 97-129
Year: 2026

Abstract:

We develop a semicontinuity-based existence theory in $\mathrm{BV}$ 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.

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