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We consider a differential operator of order 2n of the type Anu = (−1)n(au(n))(n), where a(x) > 0 in [0,1]∖{x0}and a(x0) = 0. We show that, for any n ∈ N, the operator −An generates a contractive analytic semigroup of angle π/2 on L2(0,1). Note that the domain of An depends on the type of degeneracy of a. Our theorems extend some previous results in [3] where n = 1. [ABSTRACT FROM AUTHOR]

We consider operators in divergence form, A1u = (au')', and in nondivergence form, A2u = au", provided that the coefficient a vanishes in an interior point of the space domain. Characterizing the domain of the operators, we prove that, under suitable assumptions, the operators A1 and A2, equipped with general Wentzell boundary conditions, are nonpositive and selfadjoint on spaces of L² type. [ABSTRACT FROM AUTHOR]