Subspace interpolation with applications to elliptic regularity

Abstract. In this paper, we prove new embedding results by means of sub-space interpolation theory and apply them to establishing regularity estimates for the biharmonic Dirichlet problem, and for the Stokes and the Navier-Stokes systems on polygonal domains. The main result of the paper gives a stabil-ity estimate for the biharmonic problem at the threshold index of smoothness. The classical regularity estimates for the biharmonic problem are deduced as a simple corollary of the main result. The subspace interpolation tools and tech-niques presented in this paper can be applied to establishing sharp regularity estimates for other elliptic boundary value problems on polygonal domains. 1