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

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Date
2022-01-11
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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 elasto plastic 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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SISSA 01/2022/MATE
Keywords
generalised functions with bounded variation, fracture mechanics, elastoplastic materials, semicontinuity, compact minimizing sequence
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