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.
CITATION STYLE
Percivale, D., & Tomarelli, F. (2017). Smooth and broken minimizers of some free discontinuity problems. In Springer INdAM Series (Vol. 22, pp. 431–468). Springer International Publishing. https://doi.org/10.1007/978-3-319-64489-9_17
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