instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Simultaneous approximation by smooth functions in Sobolev and Lebesgue spaces
We show how to approximate functions defined on smooth bounded domains by smooth functions in such a way that the approximations are bounded and converge in both Lebesgue spaces and $L^2$-based Sobolev spaces simultaneously. We prove an abstract result referred to fractional power spaces of positive, self-adjoint, compact-inverse operators on Hilbert spaces, and then obtain our main result by identifying explicitly these fractional power spaces for the Dirichlet Laplacian and Dirichlet Stokes operators.

This is joint work with Charles Fefferman (Princeton) and Karol Hajduk (Warwick).