We prove that the problem Minimize ∫Ω g(Φ(▽T(x)))dx, T ∈ TB + W01, ∞ (Ω, Rn) admits at least one solution for any lower-semicontinuous extended valued function g, for any quasi-affine real-valued function Φ, and for any piecewise-affine boundary datum TB such that Φ(▽TB) is constant.
Cellina, A., Zagatti, S. (1995). An existence result in a problem of the vectorial case of the calculus of variations. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 33(3), 960-970 [10.1137/S0363012993247640].
An existence result in a problem of the vectorial case of the calculus of variations
CELLINA, ARRIGO;
1995
Abstract
We prove that the problem Minimize ∫Ω g(Φ(▽T(x)))dx, T ∈ TB + W01, ∞ (Ω, Rn) admits at least one solution for any lower-semicontinuous extended valued function g, for any quasi-affine real-valued function Φ, and for any piecewise-affine boundary datum TB such that Φ(▽TB) is constant.File in questo prodotto:
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