  Given a bounded domain in the Euclidean space satisfying the uniform outer
cone condition, we show that a uniformly elliptic operator of second order with
continuous second order coefficients generates a holomorphic semigroup on the
space of all continuous functions vanishing at the boundary. In particular,
Lipschitz domains are allowed. This result was so far known under considerable
stronger regularity assumptions. Also the Dirichlet problem is considered for
such operators.
