A unified approach to degenerate problems in the half-space

We study elliptic and parabolic problems governed by the singular elliptic operators ( I L=y alpha 1Ax+y alpha 2Dyy+ycDy-b, alpha 1, alpha 2 is an element of R y2 in the half-space RN+1 + = {(x, y) : x is an element of RN, y > 0}. We prove elliptic and parabolic Lp-estimates and solvability for the associated problems. In the language of semigroup theory, we prove that L generates an analytic semigroup, characterize its domain as a weighted Sobolev space and show that it has maximal regularity.