  In this paper, we present a bootstrap procedure for general elliptic systems
with $n(\geq 3)$ components. Combining with the $L^p$-$L^q$-estimates, it
yields the optimal $L^\infty$-regularity conditions for the three well-known
types of weak solutions: $H_0^1$-solutions, $L^1$-solutions and
$L^1_\delta$-solutions. Thanks to the linear theory in $L^p_\delta(\Omega)$, it
also yields the optimal conditions for a priori estimates for
$L^1_\delta$-solutions. Based on the a priori estimates, we improve known
existence theorems for some classes of elliptic systems.
