Lower semicontinuity and existence results for anisotropic TV functionals with signed measure data
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.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Journal of Functional Analysis
- Volume
- 290
- Issue
- 8
- Pages
- 111350–111350
- Publication date
- 13 January 2026
- Language
- EN