This analysis shows Lipschitz stability and differentiability of solution maps in quasi-variational inequalities, suggesting pathways to optimal control.
Key Points
The solution maps of quasi-variational inequalities are locally Lipschitz continuous and directionally differentiable.
We establish the existence of optimal controls for problems utilizing minimal and maximal solution maps effectively.
Penalisation methods using Moreau–Yosida techniques provide a way to approximate solutions through simpler PDEs.
Lipschitz and differential stability properties hold for the solution mappings of the penalised problems.