Regularity for dual solutions and for weak cluster points of minimizing sequences of variational problems with linear growth

The minimum problem ∫Ωf(∇u)dx → min among the mappings u: ℝn ⊃ Ω → ℝN with prescribed Dirichlet boundary data and for integrands f of linear growth in general fails to have solutions in the Sobolev space W11. We therefore concentrate on the dual variational problem, which admits a unique maximizer σ, and prove the partial Hölder continuity of σ. Moreover, we study smoothness properties of the L1-limits of minimizing sequences of the original problem. ©2002 Plenum Publishing Corporation.