Degenerate second order differential operators generating analytic semigroups in Lp and W1,p


We deal with the problem of analyticity for the semigroup generated by the second order differential operator Au:= αu″ + βu′ (or by some restrictions of it) in the spaces Lp(0, 1), with or without weight, and in W1,p(0, 1), 1 < p < ∞. Here α and β are assumed real-valued and continuous in [0, 1], with α(x) > 0 in (0, 1), and the domain of A is determined by the generalized Neumann boundary conditions and by Wentzell boundary conditions.

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Mathematische Nachrichten