A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces

摘要

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 L-delta(p)(Omega) = L-p(Omega; delta(x)dx), where delta(x) is the distance to the boundary. Using this method, we significantly improve the known existence results for various classes of elliptic systems.