Lp-theory for some elliptic and parabolic problems with first order degeneracy at the boundary

Let Omega be a smooth open bounded set in R-N, let rho be the (smoothed in the interior) distance function from partial derivative Omega let (a(ij)) be a uniformly elliptic matrix with continuous entries in Omega and A the associated second order elliptic operator. Under suitable conditions, we prove that the operator L = -rho A + B, with B a first order operator with continuous coefficients, with Dirichlet boundary conditions, generates an analytic semigroup in L-p(Omega), 1 < p < infinity, and in C((Omega) over bar). In L-p(Omega) we also give a precise description of the domain. (c) 2007 Elsevier Masson SAS. All rights reserved.