| Abstract: | C [0,1], α > 0 in (0,1) and α(1), we consider the second order differential operator on C[0,1] defined by Au: = αu″ + βu′, where D(A) may include Wentzell boundary conditions. Under integrability conditions involving √α and β/√α, we prove the analyticity of the semigroup generated by (A,D(A)) on Co[0,1], Cπ[0,1] and on C[0,1], where Co[0,1]: {u∈ C[0,1]|u (1)} and Cπ[0,1]: = {u∈ C[0,1]| u (0) = u (1)}. We also prove different characterizations of D(A) related to some results in [1], where β≡ 0, exhibiting peculiarities of Wentzell boundary conditions. Applications can be derived for the case αx = x k (1 - x )kγ(x )(k≥j/2, x∈ [0,1], γ∈ C{0,1}). |
