Minimizers of abstract generalized Orlicz‐bounded variation energy

Abstract

A way to measure the lower growth rate of is to require to be increasing in . If this condition holds with , thenwith boundary values does not necessarily have a minimizer. However, if is replaced by , then the growth condition holds with and thus (under some additional conditions) the corresponding energy integral has a minimizer. We show that a sequence of such minimizers converges when in a suitable ‐type space involving generalized Orlicz growth and obtain the ‐convergence of functionals with fixed boundary values and of functionals with fidelity terms.