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.
Articolo in rivista - Articolo scientifico
Relaxed problem; minimum problem; Jacobian determinant; lower- semicontinuous extended-valued function; quasi-affine real-valued function
English
1995
33
3
960
970
none
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/19658
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