Abstract
We study elliptic operators L with Dirichlet boundary conditions on a bounded domain Ω whose diffusion coefficients degenerate linearly at ∂ Ω in tangential directions. We compute the domain of L and establish existence, uniqueness and (maximal) regularity of the elliptic and parabolic problems for L in L p -spaces and in spaces of continuous functions. Moreover, the analytic semigroups generated by L are consistent, positive, compact and exponentially stable.
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