REGULARITY OF LIPSCHITZ FREE BOUNDARIES FOR THE THIN ONE-PHASE PROBLEM.
D. De, Silva, O. Savin · 2016
We study regularity properties of the free boundary for the thin one-phase problem which consists of minimizing the energy functional E(u,\Omega) = \int_\Omega | abla u|^2 dX + \mathcal{H}^n(\{u>0\} \cap \{x_{n+1} = 0\}), \quad \Omega \subset \mathbb R^{n+1}, among all functions u\ge 0 which are fixed on \partial \Omega .