Regularity improvement for the minimizers of the two-dimensional Griffith energy
Camille Labourie, Antoine Lemenant
TL;DR
This paper proves that the singular set of connected minimizers of the planar Griffith functional is smaller than one-dimensional and establishes higher integrability of the symmetrized gradient, advancing understanding of fracture mechanics models.
Contribution
It introduces new regularity results for minimizers of the Griffith energy in two dimensions, specifically regarding the size of the singular set and gradient integrability.
Findings
Singular set of minimizers has Hausdorff dimension less than one.
Higher integrability of the symmetrized gradient is established.
Provides new regularity insights for fracture mechanics models.
Abstract
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.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows