Calculus of Variations and Geometric Measure Theory

E. Ficola - T. Schmidt

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

created by schmidt on 11 Apr 2024
modified on 29 May 2024


Submitted Paper

Inserted: 11 apr 2024
Last Updated: 29 may 2024

Year: 2024

ArXiv: 2404.07631 PDF


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.