Abstract
We present a new general method to obtain regularity and a priori estimates for solutions of semilinear elliptic systems in bounded domains. This method is based on a bootstrap procedure, used alternatively on each component, in the scale of weighted Lebesgue spaces Lpδ(Ω)=Lp(Ωδ(x) dx), where δ(x) is the distance to the boundary. Using this method, we significantly improve the known existence results for various classes of elliptic systems.
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