We show that the Lavrentiev phenomenon does not occur for functionals of the form ∫ΩL(|∇u(x)|) dx, where L is an arbitrary convex function, provided that both ∂Ω and u0 are of class C2. © de Gruyter 2013.
Bonfanti, G., Cellina, A. (2013). On the non-occurrence of the Lavrentiev phenomenon. ADVANCES IN CALCULUS OF VARIATIONS, 6, 93-121 [10.1515/acv-2011-0002].
On the non-occurrence of the Lavrentiev phenomenon
BONFANTI, GIOVANNI;CELLINA, ARRIGO
2013
Abstract
We show that the Lavrentiev phenomenon does not occur for functionals of the form ∫ΩL(|∇u(x)|) dx, where L is an arbitrary convex function, provided that both ∂Ω and u0 are of class C2. © de Gruyter 2013.
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