Minimizers of abstract generalized Orlicz‐bounded variation energy
نویسندگان
چکیده
A way to measure the lower growth rate of φ : Ω × [ 0 , ∞ ) → $$ \varphi :\Omega \times \left[0,\infty \right)\to \right) is require t ↦ ( x − r t\mapsto \left(x,t\right){t}^{-r} be increasing in \left(0,\infty . If this condition holds with = 1 r=1 then inf u ∈ f + W ∫ | ∇ d \underset{u\in f+{W}_0^{1,\varphi}\left(\Omega \right)}{\operatorname{inf}}{\int}_{\Omega}\varphi \left(x,|\nabla u|\right)\kern0.1em dx boundary values f\in {W}^{1,\varphi}\left(\Omega does not necessarily have a minimizer. However, if replaced by p {\varphi}^p > r=p>1 and thus (under some additional conditions) corresponding energy integral has We show that sequence \left({u}_p\right) such minimizers converges when p\to {1}^{+} suitable BV \mathrm{BV} -type space involving generalized Orlicz obtain Γ \Gamma -convergence functionals fixed fidelity terms.
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ژورنال
عنوان ژورنال: Mathematical Methods in The Applied Sciences
سال: 2023
ISSN: ['1099-1476', '0170-4214']
DOI: https://doi.org/10.1002/mma.9042