Existence theorems for multiple integrals of the calculus of variations for discontinuous solutions
type: Item
instance of: scholarly article
title: Existence theorems for multiple integrals of the calculus of variations for discontinuous solutions
zbMATH Open document ID: 0668.49018
DOI: 10.1007/BF01766143
author: Lamberto Cesari
author: Primo Brandi
author: Anna Salvadori
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1988-01-01T00:00:00Z
review text: We prove existence theorems for the minimum of multiple integrals of the calculus of variations with constraints on the derivatives in classes of BV possibly discontinuous solutions. To this effect the integrals are written in the form proposed by \textit{J. Serrin} [Trans. Am. Math. Soc. 101, 139--167 (1961; Zbl 0102.04601)]. Usual convexity conditions are requested, but no growth condition. Preliminary closure and semicontinuity theorems are proved. Compactness in \(L_ 1\) of classes of BV functions with equibounded total variations is derived from Cafiero-Fleming theorems.
Mathematics Subject Classification ID: 49K35
Mathematics Subject Classification ID: 49K99
Mathematics Subject Classification ID: 54C08
zbMATH DE Number: 4094250
zbMATH Keywords: multiple integrals
zbMATH Keywords: discontinuous solutions
zbMATH Keywords: convexity conditions
zbMATH Keywords: semicontinuity theorems
zbMATH Keywords: Cafiero-Fleming theorems
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4094250