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On a Neumann problem for variational functionals of linear growth
Type of publication: Article
Citation:
Publication status: Published
Journal: Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Volume: XXI
Year: 2020
Pages: 695--737
DOI: 10.2422/2036-2145.201802_005
Abstract: We consider a Neumann problem for strictly convex variational functionals of linear growth. We establish the existence of minimisers among W1,1- functions provided that the domain under consideration is simply connected. Hence, in this situation, the relaxation of the functional to the space of functions of bounded variation, which has better compactness properties, is not necessary. Similar W1,1-regularity results for the corresponding Dirichlet problem are only known under rather restrictive convexity assumptions limiting its non-uniformity up to the borderline case of the minimal surface functional, whereas for the Neumann problem no such quantified version of strong convexity is required.
Preprint project: NCMM
Preprint year: 2020
Preprint number: 13
Preprint ID: NCMM/2020/13
Keywords:
Authors Beck, Lisa
Bulíček, Miroslav
Gmeineder, Franz
Added by: [MB]
Total mark: 0
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