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Existence of discontinuous absolute minima for certain multiple integrals without growth properties

Lamberto Cesari — 1988

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the present paper the author discusses certain multiple integrals I ( u ) of the calculus of variations satisfying convexity conditions, and no growth property, and the corresponding Serrin integrals ( u ) , to which the existence theorems in [3,4,5] do not apply. However, in the present paper, the integrals I ( u ) and ( u ) are reduced to simpler form H ( v ) and ( v ) to which the existence theorems above apply. Thus, we derive that I ( u ) ( u ) , H ( v ) ( v ) , we obtain the existence of the absolute minimum for the Serrin forms ( u ) and ( v ) , and...

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