Variational inequalities with one-sided irregular obstacles

The authors show that the Hölder continuity of the solutionu∈K?{v∈H _o ¹ (Ω) | v≤ψ in Ω} of the variational inequality $$(\triangledown u,\triangledown u - \triangledown v) \leqslant (f,u - v),v\varepsilon \mathbb{K},$$ also holds under a one-sided Hölder condition on the obstacle ψ. This class of obstacles ψ contains the implicit obstacles of the quasivariational inequalities occuring in stochastic impulse control.