Inserted: 17 jan 2023
Last Updated: 2 nov 2023
Journal: Calculus of Variations and Partial Differential Equations
A lower semicontinuity result and a relaxation formula for free discontinuity functionals with non-standard growth in the bulk energy are provided. Our analysis is based on a non-trivial adaptation of the blow-up of Ambrosio (1994) and of the global method for relaxation of Bouchitté-Fonseca-Leoni-Mascarenhas (2002) to the setting of generalized special function of bounded variation with Orlicz growth. Key tools developed in this paper are an integral representation result and a Poincaré inequality under non-standard growth.