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Lower Semicontinuity in L¹ of a Class of Functionals Defined on BV with Caratheodory Integrands
Wunderli, Thomas (Hindawi Limited, 2021)We prove lower semicontinuity in 𝐿¹(Ω) for a class of functionals 𝒢 :𝐵𝑉(Ω) →ℝ of the form 𝒢(𝑢)=∫Ω𝑔(𝑥, 𝛻𝑢)𝑑𝑥 + ∫Ω𝜓(𝑥)𝑑|Dˢ𝑢| where 𝑔 :Ω⨉ℝᴺ→ℝ, Ω⊂ℝᴺ is open and bounded, 𝑔(.,𝑝) ∊ 𝐿¹(Ω) for each 𝑝 satisfies ...