Higher Regularity for Fractional Powers of the Laplacian

This chapter is devoted to the study of regularity properties of fractional powers of the Laplacian subject to mixed boundary conditions on an interior thick and open set \({\boldsymbol {O}} \subseteq \mathbb {R}^d\) . Our main motivation is its application in Chap. 12 , but in light of the growing interest in fractional Laplacians in other fields of analysis, this might also be of independent interest.