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@ARTICLE{,
            author = {Beck, Lisa and Bul{\'{\i}}{\v c}ek, Miroslav and Gmeineder, Franz},
             title = {On a Neumann problem for variational functionals of linear growth},
           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}
}