A unified approach to degenerate problems in the half-space

We study elliptic and parabolic problems governed by the singular operatorsL=yα1Δx+yα2(Dyy+cyDy−by2),α1,α2∈R in half-space R+N+1={(x,y):x∈RN,y>0}. prove Lp-estimates solvability for associated problems. In language of semigroup theory, we that L generates an analytic semigroup, characterize its domain as a weighted Sobolev space show it has maximal regularity.