arXiv subjects

Eleonora Ficola

Publications and source records attributed to Eleonora Ficola.

2 recordsLinked to original sources

arXiv2026

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

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.

math.AP↗

arXiv2026

Lower semicontinuity and existence results for anisotropic TV functionals with signed measure data

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.

math.AP↗