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

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.

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Correspondence to D. Apushkinskaya.

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Translated from Problems in Mathematical Analysis 44, January 2010, pp. 39–54.

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Apushkinskaya, D., Bildhauer, M. & Fuchs, M. On local generalized minimizers and local stress tensors for variational problems with linear growth. J Math Sci 165, 42–59 (2010). https://doi.org/10.1007/s10958-010-9779-2

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Keywords

  • Variational Problem
  • Linear Growth
  • Boundary Data
  • Generalize Minimizer
  • Dual Solution