We prove that the Lavrentiev phenomenon does not occur for the functional ∫Ω[l(|∇ u(x)|) + G(u)] dx on u - u0 ∈ W1,10 (Ω), where L and G are convex functions subject to additional regularity assumptions, and where ∂Ω and u 0 are smooth. © 2013 Society for Industrial and Applied Mathematics.
Bonfanti, G., Cellina, A. (2013). The nonoccurrence of the Lavrentiev phenomenon for a class of variational functionals. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 51, 1639-1650 [10.1137/12086618X].
The nonoccurrence of the Lavrentiev phenomenon for a class of variational functionals
BONFANTI, GIOVANNI;CELLINA, ARRIGO
2013
Abstract
We prove that the Lavrentiev phenomenon does not occur for the functional ∫Ω[l(|∇ u(x)|) + G(u)] dx on u - u0 ∈ W1,10 (Ω), where L and G are convex functions subject to additional regularity assumptions, and where ∂Ω and u 0 are smooth. © 2013 Society for Industrial and Applied Mathematics.
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