Lower Semicontinuity in L1 of a Class of Functionals Defined on BV with Carathéodory Integrands
We prove lower semicontinuity in L1Ω for a class of functionals G:BVΩ⟶ℝ of the form Gu=∫Ωgx,∇udx+∫ΩψxdDsu where g:Ω×ℝN⟶ℝ, Ω⊂ℝN is open and bounded, g·,p∈L1Ω for each p, satisfies the linear growth condition limp⟶∞gx,p/p=ψx∈CΩ∩L∞Ω, and is convex in p depending only on p for a.e. x. Here, we recall fo...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2021/6709303 |
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