Abstract:It is well known that the inf-sup condition is a fundamental result in the variational analysis of the Stokes equations. This condition has been widely studied by several authors with different assumptions on the domains. For example, it has been proved that it is valid on Lipschitz domains but fails on cuspidal ones.
In this talk we will show some weak inf-sup conditions on cuspidal domains using weighted Sobolev spaces, and how these can be applied to obtain results on the well posedness of the Stokes equations.