On the Lavrentiev phenomenon
type: Item
instance of: scholarly article
title: On the Lavrentiev phenomenon
zbMATH Open document ID: 0585.49003
DOI: 10.1007/BF02576198
published in: Calcolo
publication date: 1985-01-01T00:00:00Z
review text: An additional assumption, besides convexity and coercivity, is formulated to guarantee that the Lavrentiev phenomenon does not occur in a basic problem of the calculus of variations. It is shown that this property \({\mathcal D}\) is weaker than a number of known conditions.
Mathematics Subject Classification ID: 49J05
Mathematics Subject Classification ID: 26A46
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 3937905
zbMATH Keywords: convexity
zbMATH Keywords: coercivity
zbMATH Keywords: Lavrentiev phenomenon
zbMATH Keywords: calculus of variations
author: Lamberto Cesari
author: Thomas S. Angell
reviewed by: Andreas Kirsch
MaRDI profile type: Publication
cites work: Q4743352
cites work: Sopra il problema dell'approssimazione delle curve dello spazio e degli integrali
cites work: Closure theorems without seminormality conditions
cites work: An existence theorem in the calculus of variations based on Sobolev's imbedding theorems
cites work: Remarks on the direct method of the calculus of variations
cites work: A note on approximation of optimal solutions of free problems of the calculus of variations
cites work: Singular minimizers for regular one-dimensional problems in the calculus of variations
cites work: Q3717698
cites work: Regularity Properties of Solutions to the Basic Problem in the Calculus of Variations
cites work: Remarks on some existence theorems for optimal control
cites work: Integrals which are convex functionals
cites work: Lower semicontinuity and lower closure theorems without seminormality conditions
cites work: Q4759873
cites work: Q4760429
cites work: Q5835150
description: scientific article; zbMATH DE number 3937905