On local generalized minimizers and local stress tensors for variational problems with linear growth

Abstract

Uniqueness and regularity results for local vector-valued generalized minimizers and for local stress tensors associated to variational problems with linear growth conditions are established. If the energy density f has structure f(Z) = h(|Z|), only very weak ellipticity assumptions are required. For the proof we combine arguments from measure theory and convex analysis with regularity results obtained by the authors recently. Bibliography: 33 titles.