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Erschienen in:
Rate of Convergence for Eigenfunctions of Aharonov-Bohm Operators with a Moving Pole Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Smooth and Broken Minimizers of Some Free Discontinuity Problems

verfasst von : Danilo Percivale, Franco Tomarelli

Erschienen in: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Verlag: Springer International Publishing

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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.

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Vorheriges Kapitel Weak Formulation for Singular Diffusion Equation with Dynamic Boundary Condition
Nächstes Kapitel Stability Results for Abstract Evolution Equations with Intermittent Time-Delay Feedback
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Metadaten
Titel
Smooth and Broken Minimizers of Some Free Discontinuity Problems
verfasst von
Danilo Percivale
Franco Tomarelli
Copyright-Jahr
2017
Buch
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Print ISBN: 978-3-319-64488-2

Electronic ISBN: 978-3-319-64489-9

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-64489-9_17