Calculus of Variations and Geometric Measure Theory

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
modified on 11 Jul 2023


Published Paper

Inserted: 11 jan 2022
Last Updated: 11 jul 2023

Journal: NoDEA Nonlinear Differential Equations Appl.
Volume: 29
Number: Paper No. 63.
Year: 2022


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.