Submitted Paper

Inserted: 11 apr 2024
Last Updated: 12 apr 2024

Year: 2024

Abstract:

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.

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• TV_phi_mu.pdf