Measure and Dimension of the Free Boundary
Bozhidar Velichkov · Lecture notes of the Unione Matematica Italiana · 2022
Abstract This chapter is dedicated to the measure theoretic structure of the free boundary ∂ Ωu. The results presented here are mainly a consequence of the Lipschitz continuity and the non-degeneracy of the minimizer u (Theorem 3.1 and Proposition 4.1 ).