is it true that the Laplacian $\Delta:=\frac{d^2}{dx^2}$ on $(0,1)$ with Neumann boundary conditions is dissipative on $C[0,1]?$


For this we have to show that there is for any $x \in D(\Delta)$a $x' \in C[0,1]'$ such that 
$x'(x)=\left\lVert x\right\rVert^2=\left\lVert x'\right\rVert^2$ and 
$$\Re \langle \Delta x,x' \rangle \le 0.$$


Does anybody know how to choose this x'?



Laplacian dissipative?
See the example of Section II.3.30 in


*Engel, Klaus-Jochen; Nagel, Rainer*, [**One-parameter semigroups for linear evolution equations**](http://dx.doi.org/10.1007/b97696), Graduate Texts in Mathematics. 194. Berlin: Springer. xxi, 586 p. (2000). [ZBL0952.47036](https://zbmath.org/?q=an:0952.47036).


