The Bounded Slope Condition for Functionals Depending on x , u , and $ ablau$
Alice Fiaschi, Giulia Treu · SIAM Journal on Control and Optimization · 2012
A global regularity result is proved for a class of minimizers of functionals of the form $\mathcal I(u)=\int_\Omega f(| abla u(x)|)+g(x,u(x))\,dx, u\in\phi+W^{1,1}_0(\Omega)$, where $\phi$ satisfies the Bounded Slope Condition.