The heat equation with generalized Wentzell boundary condition

Let Ω be a bounded subset of RN, a ε C1 (Ω) with a \u3e 0 in Ω and A be the operator defined by Au := ∇ · (a∇u) with the generalized Wentzell boundary condition equation presented If ∂Ω is in C2, β and γ are nonnegative functions in C1 (∂Ω), with β \u3e 0, and Γ := {x ε ∂Ω : a(x) \u3e 0] ≠ ø, then we prove the existence of a (Co) contraction semigroup generated by Ā, the closure of A, on a suitable Lp space, 1 ≤ p \u3c ∞ and on C(Ω). Moreover, this semigroup is analytic if 1 \u3c p \u3c ∞