Lipschitz regularity of almost minimizers in a Bernoulli problem with non-standard growth
Lipschitz regularity of almost minimizers in a Bernoulli problem with non-standard growth
In this work we establish the optimal Lipschitz regularity for non-negative almost minimizers of the one-phase Bernoulli-type functional$ \mathcal{J}_{\mathrm{G}}(u, \Omega) \mathrel{\mathop:} = \displaystyle{\int}_\Omega \left(\mathrm{G}(|\nabla u|)+\chi_{\{u>0\}}\right)\, dx $where $ \Omega \subset \mathbb{R}^n $ is a bounded domain and $ \mathrm{G}: [0, \infty) \to [0, \infty) $ is a Young function with …