Abstract
The existence theorem of Fichera for the minimum problem of semicoercive quadratic functions in a Hilbert space is extended to a more general class of convex and lower semicontinuous functions. For unbounded domains, the behavior at infinity is controlled by a lemma which states that every unbounded sequence with bounded energy has a subsequence whose directions converge to a direction of recession of the function. Thanks to this result, semicoerciveness plus the assumption that the effective domain is boundedly generated, that is, admits a Motzkin decomposition, become sufficient conditions for existence. In particular, for functions with a smooth quadratic part, a generalization of the existence condition given by Fichera’s theorem is proved.
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Communicated by Victor Eremeyev, Peter Schiavone and Francesco dell'Isola.
Dedicated to the memory of Jean-Jacques Moreau.
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Piero, G.D. Minimization of semicoercive functions: a generalization of Fichera’s existence theorem for the Signorini problem. Continuum Mech. Thermodyn. 28, 5–17 (2016). https://doi.org/10.1007/s00161-014-0379-0
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DOI: https://doi.org/10.1007/s00161-014-0379-0