A1 Refereed original research article in a scientific journal
Minimizers of abstract generalized Orlicz-bounded variation energy
Authors: Eleuteri Michela, Harjulehto Petteri, Hästö Peter
Publisher: Wiley
Publication year: 2022
Journal: Mathematical Methods in the Applied Sciences
Journal name in source: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Journal acronym: MATH METHOD APPL SCI
Number of pages: 15
ISSN: 0170-4214
eISSN: 1099-1476
DOI: https://doi.org/10.1002/mma.9042
Web address : https://onlinelibrary.wiley.com/doi/10.1002/mma.9042
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/178878073
Preprint address: https://arxiv.org/abs/2112.06622
A way to measure the lower growth rate of phi : Omega x [0, infinity) -> [0, infinity) is to require t (sic) phi (x, t)t(-r) to be increasing in (0, infinity). If this condition holds with r = 1, theninf (u is an element of f+W1,phi (Omega)) integral(Omega) phi(x, vertical bar del u vertical bar) dxwith boundary values f is an element of W-1,W-phi (Omega) does not necessarily have a minimizer. However, if phi is replaced by phi(p), then the growth condition holds with r = p > 1 and thus (under some additional conditions) the corresponding energy integral has a minimizer. We show that a sequence (u(p)) of such minimizers converges when p -> 1(+) in a suitable BV-type space involving generalized Orlicz growth and obtain the Gamma-convergence of functionals with fixed boundary values and of functionals with fidelity terms.
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