Local Lipschitz continuity of the minimizers of nonuniformly convex functionals under the Lower Bounded Slope Condition

Flavia Giannetti, Giulia Treu

We prove the local Lipschitz regularity of the minimizers of functionals of the form \[ \mathcal I(u)=\int_Ωf(\nabla u(x))+g(x)u(x)\,dx\qquad u\inϕ+W^{1,1}_0(Ω) \] where $g$ is bou…