$H^{-3/2}$ control of the laplacian of a function by means of $H^{1/2}$ norm in $\mathbb{R}^2$

Question

I am wondering for my research if, given a smooth bounded domain $\Omega\subset\mathbb{R}^2$ then, for a sufficiently regular function $u$ we can write $$ \Vert \Delta u\Vert_{H^{-3/2}(\Omega)}\leq C\Vert u \Vert_{H^{1/2}(\Omega)}, $$ for some positive constant $C$. I know a similar result related to the control of $H^{-1}$ norm, which can be obtained by duality, but in the fractional case I do not know how to proceed.

Thank you!