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A priori Estimates and Existence for Elliptic Systems via Bootstrap in Weighted Lebesgue Spaces

Authors:	P?Quittner Email author" target="_blank">Ph?Souplet Email author

Institution:	(1) Institute of Applied Mathematics, Comenius University, Mlynská dolina, 84248, Bratislava, Slovakia;(2) Laboratoire de Mathématiques Appliquées UMR CNRS 7641, Université de Versailles, 45 avenue des Etats-Unis, 78035 Versailles, France

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 L^p()=L^p((x)dx), where (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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