We present uniform regularity results regarding positive solutions of the family of systems
\[
\begin{cases}
-\Delta u_{i,\beta} = f_{i,\beta}(u_{i,\beta}) -\beta u_{i,\beta} \sum_{j \neq i} a_{ij} u_{j,\beta}^p & \text{in \(\Omega\)} \\
u_{i,\beta}=0 & \text{on \(\partial \Omega\)} \qquad i=1,\dots,k
\end{cases}
\]
in the cases \(p=1\) (symmetric interaction) and \(p=2\) (variational interaction). For such systems, of interest in population dynamics and in the study of phase-separation of Bose-Einstein condensates, we show that \(L^\infty(\Omega)\)-boundedness implies \(\mathcal{C}^{0,1}(\overline{\Omega})\)-boundedness, uniformly in \(\beta \to +\infty\). This extend the \(\mathcal{C}^{0,\alpha}\)-regularity theory available in the literature (\(0 \le \alpha <1\)) to the optimal Lipschitz case.
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