WIAS Preprint No. 1664, (2011)

Global higher integrability of minimizers of variational problems with mixed boundary conditions


  • Fiaschi, Alice
  • Knees, Dorothee
  • Reichelt, Sina

2010 Mathematics Subject Classification

  • 74C05 49N60 49S05 35B65


  • Higher integrability of gradients of minimizers, p-growth, mixed boundary conditions, damage, uniform Caccioppoli-like inequality


We consider integral functionals with densities of p-growth, with respect to gradients, on a Lipschitz domain with mixed boundary conditions. The aim of this paper is to prove that, under uniform estimates within certain classes of p-growth and coercivity assumptions on the density, the minimizers are of higher integrability order, meaning that they belong to the space of first order Sobolev functions with an integrability of order p+ε for a uniform ε >0. The results are applied to a model describing damage evolution in a nonlinear elastic body and to a model for shape memory alloys.

Appeared in

  • J. Math. Anal. Appl., 401 (2013) pp. 269--288.

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