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

The optimal local Lipschitz regularity for scalar almost-minimizers of Alt-Caffarelli-type functionals $$\mathcal{F}(v;\mathrm{\Omega })={\int }_{\mathrm{\Omega }}\phi (x,\mid \mathrm{\nabla }v(x)\mid )+\lambda {\chi }_{\{v>0\}}(x)\mathrm{d}x,$$ with growth function $\phi$ a generalized Orlicz function, is established.