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arXiv · 2505.11279

Existence theory for linear-growth variational integrals with signed measure data

Eleonora Ficola·Thomas Schmidt
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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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Eleonora Ficola, Thomas Schmidt. 2025-05-16. Existence theory for linear-growth variational integrals with signed measure data. https://doi.org/10.1515/acv-2025-0057

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