Improved convergence rates in the fast-reaction approximation of the triangular Shigesada-Kawasaki-Teramoto system

We consider the fast-reaction approximation to the triangular Shigesada-Kawasaki-Teramoto model on a bounded domain in the physical dimension $d\le 3$. We provide explicit convergence rates on the whole domain in ${\text{L}}^{\mathrm{\infty }}{\text{L}}^2\cap {\text{L}}^2{\text{H}}^1$ and in the interior we prove convergence with an explicit rate in any ${\text{L}}^{\mathrm{\infty }}{\text{H}}^l$ for all $l>0$.