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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
1/2000

Conditions for equality of hulls in the calculus of variations

Georg Dolzmann, Bernd Kirchheim and Jan Kristensen

Abstract

We simplify and sharpen several results by K. Zhang concerning properties of quasiconvex hulls of sets and quasiconvex envelopes of their distance functions. The approach emphasizes the underlying geometry and in particular we show that Kpc=Kc implies Krc=Kc if and only if min{m,n} <= 2 thus answering a question raised in
K.W. Zhang, On various semiconvex hulls in the calculus of variations, Calc. Var. PDE 6 (1998), 143 - 160.

Received:
Jan 6, 2000
Published:
Jan 6, 2000
MSC Codes:
26B15, 74N15
Keywords:
gradient young measures, quaiconvex hull, distance function

Related publications

inJournal
2000 Repository Open Access
Georg Dolzmann, Bernd Kirchheim and Jan Kristensen

Conditions for equality of hulls in the calculus of variations

In: Archive for rational mechanics and analysis, 154 (2000) 2, pp. 93-100