Speaker
Description
Weak solutions of the 2D eikonal equation correspond to unit vector fields $m$ with zero divergence in the sense of distributions. They arise naturally as sharp interface limits of bounded energy configurations in micromagnetics, elasticity or liquid crystal models (e.g. Aviles-Giga). For a given weak solution $m$, entropy productions are distributions which carry information about singularities and energy cost. If they are signed measures, it is conjectured that they must be concentrated on the 1-rectifiable jump set of $m$, as they do if $m$ has bounded variation (BV). In a joint work with Elio Marconi, we prove this concentration property under an additional mild regularity assumption, going well beyond the BV setting, and leaving only a borderline case open.
