Optimal conditions for L∞-regularity and a priori estimates for semilinear elliptic systems

In this paper, we present a bootstrap procedure for semilinear elliptic systems with n (>= 3) components. Combining with the L-p-L-q-estimates, if yields the optimal L-infinity-regularity conditions for the three well known types of weak Solutions: H-0(1)-soultions, L-1-solutions and L-delta(1)-solutions. Thanks to the linear theory in L-delta(p)(Omega), it also yields the optimal conditions for a priori estimates for L-delta(1)-solutions. Based on the a priori estimates, we improve known existence theorems for some classes of elliptic systems. (c) 2008 Elsevier Inc. All rights reserved.