Orateur
Description
The Aviles-Giga energy is a phase transition model related to liquid crystals, micromagnetics and elasticity. Sharp interface limits of bounded energy are weak solutions of the 2D eikonal equation: unit vector fields $m$ with zero divergence (in the sense of distributions). Partial information about the limit energy cost of a given solution $m$ is encoded in a family of signed measures called entropy productions. It is conjectured that these measures are 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.
