We consider the existence of solutions, in the space W1,1(Ω), to the problemminimize öΩL(v(x))dxonφ+W01,1(Ω) where L is of slow (linear or at most quadratic) growth. We present a necessary and sufficient condition in order that, for any smooth boundary datum φ and for any bounded Ω with smooth boundary, the minimum problem be solvable.

Staicu, V., Cellina, A. (2016). The existence of solutions to variational problems of slow growth. JOURNAL OF DIFFERENTIAL EQUATIONS, 260(7), 5834-5846 [10.1016/j.jde.2015.12.025].

The existence of solutions to variational problems of slow growth

CELLINA, ARRIGO
2016

Abstract

We consider the existence of solutions, in the space W1,1(Ω), to the problemminimize öΩL(v(x))dxonφ+W01,1(Ω) where L is of slow (linear or at most quadratic) growth. We present a necessary and sufficient condition in order that, for any smooth boundary datum φ and for any bounded Ω with smooth boundary, the minimum problem be solvable.
Articolo in rivista - Articolo scientifico
Calculus of Variations
English
5834
5846
13
Staicu, V., Cellina, A. (2016). The existence of solutions to variational problems of slow growth. JOURNAL OF DIFFERENTIAL EQUATIONS, 260(7), 5834-5846 [10.1016/j.jde.2015.12.025].
Staicu, V; Cellina, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/141308
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