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Smooth and Broken Minimizers of Some Free Discontinuity Problems

  • Danilo Percivale
  • Franco TomarelliEmail author
Chapter
Part of the Springer INdAM Series book series (SINDAMS, volume 22)

Abstract

We show that minimizers of free discontinuity problems with energy dependent on jump integrals and Dirichlet boundary conditions are smooth provided a smallness condition is imposed on data. We examine in detail two examples: the elastic-plastic beam and the elastic-plastic plate with free yield lines. In both examples there is a gap between the condition for solvability (safe load condition) and this smallness condition (load regularity condition) which imply regularity and uniqueness of minimizers. Such gap allows the existence of damaged/creased minimizers. Eventually we produce explicit examples of irregular solutions when the load is in the gap.

Keywords

Bounded Hessian functions Free discontinuity problem Safe load condition Regular minimizers Broken minimizers Plastic hinges in a beam 

AMS (MOS) Subject Classification (2010)

49J10 74K20 74K30 74R99 74C99 

Notes

Acknowledgements

This paper is dedicated to Gianni Gilardi on the occasion of his 70th Birthday.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria MeccanicaUniversità di GenovaGenovaItaly
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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