Submitted Paper

Inserted: 16 may 2025
Last Updated: 19 may 2025

Year: 2025

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.

Download:

• Existence for linear-growth integrals with measures.pdf