Boundary singular sets for Stokes equations (Q2771090)

For Stokes equations, the authors study relations between the size of removable singular sets on the boundary and their removability. After proving that the capacity function belongs to a fractional Sobolev space, the author demonstrate that singular sets with sufficiently small capacity are removable to fractional Sobolev solutions. Then the fact that Poisson kernel for Stokes equations maps the capacity measures on the boundary to a suitable fractional Sobolev space in the whole domain allows the authors to formulate a removability criterion in terms of capacity of singular sets for sufficiently regular Sobolev solutions.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00046].