The paper is devoted to determining necessary and sufficient conditions for existence of solutions to the problem $ inf{ m ess sup_{xin Omega} f( abla u(x)) : u in u_0 + W^{1,infty}_0 (Omega)}, when the supremand $f$ is not necessarily level convex. These conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum. Several conditions of convexity for the supremand $f$ are also investigated.

Existence of minimizers for non-level convex supremal functionals / Ribeiro Ana, Margarida; Zappale, Elvira. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 52:5(2014), pp. 3341-3370. [10.1137/13094390X]

Existence of minimizers for non-level convex supremal functionals

ZAPPALE, ELVIRA
2014

Abstract

The paper is devoted to determining necessary and sufficient conditions for existence of solutions to the problem $ inf{ m ess sup_{xin Omega} f( abla u(x)) : u in u_0 + W^{1,infty}_0 (Omega)}, when the supremand $f$ is not necessarily level convex. These conditions are obtained through a comparison with the related level convex problem and are written in terms of a differential inclusion involving the boundary datum. Several conditions of convexity for the supremand $f$ are also investigated.
2014
supremal functionals, level convexity
01 Pubblicazione su rivista::01a Articolo in rivista
Existence of minimizers for non-level convex supremal functionals / Ribeiro Ana, Margarida; Zappale, Elvira. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - 52:5(2014), pp. 3341-3370. [10.1137/13094390X]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1458192
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