The heat equation with generalized Wentzell boundary condition

Let Omega be a bounded subset of R-N, a is an element of C-1 ((Omega) over bar) with a > 0 in Omega and A be the operator defined by Au := del.(adelu) with the generalized Wentzell boundary condition Au + beta partial derivativeu/partial derivativen + yu = 0 on partial derivativeOmega If partial derivativeOmega is in C-2, beta and gamma are nonnegative functions in C-1 (partial derivativeOmega), with beta > 0, and Gamma := {x is an element of partial derivativeOmega: a(x) > 0} not equal 0, then we prove the existence of a (C-0) contraction semigroup generated by (A) over bar, the closure of A, on a suitable L-P space, 1 less than or equal to p < infinity and on C(<(Omega)over bar>). Moreover, this semigroup is analytic if 1 < p < infinity.