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.

Smooth and Broken Minimizers of Some Free Discontinuity Problems

Tomarelli, Franco
2017

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.
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs
978-3-319-64488-2
978-3-319-64489-9
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1037762
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