|Dept.||KTH(Royal Institute of Technology)|
We consider almost minimizers for the thin obstacle problem with variable Hölder continuous coefficients and zero thin obstacle. We discuss the regularity of almost minimizers, as well as the regularity and structure of their free boundaries. The analysis of the free boundary is based on Weiss- and Almgren-type monotonicity formulas, and epiperimetric inequalities. This is joint work with Arshak Petrosyan and Mariana Smit Vega Garcia.