  In this paper we consider the initial boundary value problem of the
Korteweg-de Vries equation posed on a finite interval \begin{equation}
u_t+u_x+u_{xxx}+uu_x=0,\qquad u(x,0)=\phi(x), \qquad 0<x<L, \ t>0 \qquad (1)
\end{equation} subject to the nonhomogeneous boundary conditions,
\begin{equation}
  B_1u=h_1(t), \qquad B_2 u= h_2 (t), \qquad B_3 u= h_3 (t) \qquad t>0 \qquad
(2)
  \end{equation} where \[ B_i u =\sum _{j=0}^2 \left(a_{ij} \partial ^j_x
u(0,t) + b_{ij} \partial ^j_x u(L,t)\right), \qquad i=1,2,3,\] and $a_{ij}, \
b_{ij}$ $ (j,i=0, 1,2,3)$ are real constants. Under some general assumptions
imposed on the coefficients $a_{ij}, \ b_{ij}$, $ j,i=0, 1,2,3$, the IBVPs
(1)-(2) is shown to be locally well-posed in the space $H^s (0,L)$ for any
$s\geq 0$ with $\phi \in H^s (0,L)$ and boundary values $h_j, j=1,2,3$
belonging to some appropriate spaces with optimal regularity.
