Calculus of Variations and Geometric Measure Theory
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G. Dal Maso - R. Toader

A new space of generalised functions with bounded variation motivated by fracture mechanics

created by dalmaso on 11 Jan 2022

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Submitted Paper

Inserted: 11 jan 2022
Last Updated: 11 jan 2022

Year: 2022

Abstract:

We introduce a new space of generalised functions with bound\-ed variation to prove the existence of a solution to a minimum problem that arises in the variational approach to fracture mechanics in elastoplastic materials. We study the fine properties of the functions belonging to this space and prove a compactness result. In order to use the Direct Method of the Calculus of Variations we prove a lower semicontinuity result for the functional occurring in this minimum problem. Moreover, we adapt a nontrivial argument introduced by Friedrich to show that every minimizing sequence can be modified to obtain a new minimizing sequence that satisfies the hypotheses of our compactness result.


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