Minimizers of abstract generalized Orlicz‐bounded variation energy

Author:

Eleuteri Michela1,Harjulehto Petteri2,Hästö Peter3ORCID

Affiliation:

1. Dipartimento di Scienze Fisiche, Informatiche e Matematiche Università degli Studi di Modena e Reggio Emilia Italy

2. Department of Mathematics and Statistics FI‐00014 University of Helsinki Helsinki Finland

3. Department of Mathematics and Statistics FI‐20014 University of Turku Turku Finland

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.

Funder

Jenny ja Antti Wihurin Rahasto

Publisher

Wiley

Subject

General Engineering,General Mathematics

Reference29 articles.

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