<div class="csl-bib-body">
<div class="csl-entry">Davoli, E., Almi, S., Kubin, A., & Tasso, E. (2025, February 11). <i>On De Giorgi’s conjecture of nonlocal approximations for free-discontinuity problems: The symmetric gradient case</i> [Conference Presentation]. XXXIV Convegno Nazionale di Calcolo delle Variazioni (CNCdV 2025), Riccione, Italy.</div>
</div>
-
dc.identifier.uri
http://hdl.handle.net/20.500.12708/212830
-
dc.description.abstract
In this talk, we show that E. De Giorgi’s conjecture for the nonlocal approximation of freediscontinuity problems extends to the case of functionals defined in terms of the symmetric gradient of the admissible field. After introducing a suitable class of continuous finite-difference approximants, we prove the compactness of eformations with equibounded energies, as well as their Gamma-convergence. The compactness analysis relies on a generalization of a Fr ́echet-Kolmogorov approach. An essential difficulty is the identification of the limiting space of admissible deformations. We show that if the approximants involve superlinear contributions, a limiting GSBD representation can be ensured, whereas a further integral geometric term appears in the limiting functional in the linear case. We eventually discuss the connection between this latter setting and an open problem in the theory of integral geometric measures.
en
dc.language.iso
en
-
dc.subject
Nonlocal functionals
en
dc.subject
Griffith functionals
en
dc.subject
De Giorgi conjecture
en
dc.title
On De Giorgi's conjecture of nonlocal approximations for free-discontinuity problems: The symmetric gradient case
