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