Regularity improvement for the minimizers of the two-dimensional griffith energy

Camille Labourie (1) , Antoine Lemenant (2)

1 UCY - University of Cyprus [Nicosia]
2 IECL - Institut Élie Cartan de Lorraine

In this paper we prove that the singular set of connected minimizers of the planar Griffith functional has Hausdorff dimension strictly less then one, together with the higher integrability of the symetrized gradient.

Mots clés: Calculus of variations; Free discontinuity problems; Griffith energy

Domaines: Equations aux dérivées partielles [math.AP]

Camille Labourie, Antoine Lemenant. Regularity improvement for the minimizers of the two-dimensional griffith energy. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 2023, ⟨10.4171/rlm/1009⟩. ⟨hal-03448933v2⟩