On second-order elliptic operators with complete first-order boundary degeneration and strong outward drift

Second order elliptic operators and their parabolic counterparts are studied in the case of complete boundary degeneration of the leading order coefficients in the presence of a strong outward pointing drift. It is shown that the problem generates a positive analytic (C_0)-semigroup with maximal (L_p)-regularity in (L_q)-spaces. This result is based on hard analysis estimates for integral operators in combination with modern functional analytic tools like ({mathcal R})-boundedness and the operator-valued functional calculus.