De Rham intersection cohomology for general perversities

For a stratified pseudomanifold $X$, we have the de Rham Theorem $\text{lau}\text{IH}\ast \text{per}pX=\text{lau}\text{IH}\text{per}t-\text{per}p\ast X,$ for a perversity $\text{per}p$ verifying $\text{per}0\le \text{per}p\le \text{per}t$, where $\text{per}t$ denotes the top perversity. We extend this result to any perversity $\text{per}p$. In the direction cohomology $\mapsto$ homology, we obtain the isomorphism $$\text{lau}\text{IH}\ast \text{per}pX=\text{lau}\text{IH}\text{per}t-\text{per}p\ast X,\text{ib}X\text{per}p,$$ where $ {\displaystyle \ib{X}{\per{p}} = \bigcup_{S \preceq S_{1} \atop \per{p} (S_{1})< 0}S = \bigcup_{\per{p} (S)< 0}\bar{S}.} $Inthedirectionhomology$\mapsto$ cohomology, we obtain the isomorphism $$\text{lau}\text{IH}\text{per}p\ast X=\text{lau}\text{IH}\ast \max (\text{per}0,\text{per}t-\text{per}p)X\mathrm{.}$$ In our paper stratified pseudomanifolds with one-codimensional strata are allowed.