let $d$ be a relatively compact $c^2$ domain in a complex manifold $x$ of dimension $n$. assume that $h^1(d,\theta)$ vanishes, where $\theta$ is the sheaf of germs of holomorphic tangent fields of $d$. suppose that the levi-form of the boundary $b d$ has at least $3$ negative eigenvalues or at least $n-1$ positive eigenvalues pointwise. we will show that if a formally integrable  almost complex structure $h$ of the holder class $c^r$ with $r>5/2$ on $d$ is sufficiently close to the complex structure on $d$, there is a embedding $f$ from $d$ into $x$ that transforms the almost complex structure into the complex structure on $f(d)$, where  $f $ has class $c^s$ for all $s<r+1/2$. this result was due to r. hamilton in the 1970s when both $b d$ and $h$ are of class $c^\infty$.