TY  - JOUR
T1  - On a Neumann problem for variational functionals of linear growth
A1  - Beck, Lisa
A1  - Bulíček, Miroslav
A1  - Gmeineder, Franz
JA  - Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)
Y1  - 2020
VL  - XXI
SP  - 695
EP  - 737
M2  - doi: 10.2422/2036-2145.201802_005
N2  - 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.
M1  - Preprint project = NCMM
M1  - Preprint year = 2020
M1  - Preprint number = 13
M1  - Preprint ID = NCMM/2020/13
ER  -