Lipschitz regularity of almost-minimizers in one-phase problems with generalized Orlicz growth

Abstract

The optimal local Lipschitz regularity for scalar almost-minimizers of Alt-Caffarelli-type functionals $$\mathcal{F}(v;\hat{I}\text{c◯})={\int }_{\hat{I}}\text{c◯}\ddot{I}†(x,\left|\nabla v(x)\right|)+\hat{I}»\ddot{I}{‡}_{\{v>0\}}(x)\mathrm{d}x,$$ with growth function $\ddot{I}†$ a generalized Orlicz function, is established.

31 pages