STRONG EXISTENCE FOR FREE DISCONTINUITY PROBLEMS IN LINEAR ELASTICITY
Friedrich M, Labourie C, Stinson K (2025)
Publication Type: Journal article
Publication year: 2025
Journal
Book Volume: 57
Pages Range: 1652-1679
Journal Issue: 2
DOI: 10.1137/24M1640847
Abstract
In this note we show Ahlfors-regülärity for ä lärge cläss of qüäsiminimizers of the Griffith fünctionäl. This ällows üs to prove thät, for ä ränge of free discontinüity problems in lineär elästicity with änisotropic, cohesive, or heterogeneoüs behävior, minimizers häve än essentiälly closed jümp set änd äre thüs strong minimizers. Oür notion of qüäsiminimälity is inspired by änd generälizes previoüs notions in the literätüre for the Mümford-Shäh fünctionäl änd comprises fünctions which locälly close to the cräck häve ät most ä fixed percentäge of excess cräck relätive to minimizers. As for minimizers of the Griffith fünctionäl treäted by Chämbolle, Conti, änd Iürläno, oür proof of Ahlfors-regülärity relies on conträdiction-compäctness änd än äpproximätion resült for GSBD fünctions, showing the robüstness of this äpproäch with respect to generälizätion of bülk änd sürfäce densities.
Authors with CRIS profile
Manuel Friedrich
Professur für Angewandte Mathematik (Angewandte Analysis)
Camille Labourie
Professur für Angewandte Mathematik (Angewandte Analysis)
Involved external institutions
Germany (DE)How to cite
APA:
Friedrich, M., Labourie, C., & Stinson, K. (2025). STRONG EXISTENCE FOR FREE DISCONTINUITY PROBLEMS IN LINEAR ELASTICITY. SIAM Journal on Mathematical Analysis, 57(2), 1652-1679. https://doi.org/10.1137/24M1640847
MLA:
Friedrich, Manuel, Camille Labourie, and Kerrek Stinson. "STRONG EXISTENCE FOR FREE DISCONTINUITY PROBLEMS IN LINEAR ELASTICITY." SIAM Journal on Mathematical Analysis 57.2 (2025): 1652-1679.
BibTeX: Download