A priori Estimates and Existence for Elliptic Systems via Bootstrap in Weighted Lebesgue Spaces
Source: Archive for Rational Mechanics and Analysis, Volume 174, Number 1, October 2004 , pp. 49-81(33)
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 Lp(Ω)=Lp(Ω(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.
Document Type: Research Article
Affiliations: 1: Institute of Applied Mathematics, Comenius University, Mlynská dolina, 84248, Bratislava, Slovakia, Email: firstname.lastname@example.org 2: Laboratoire de Mathématiques Appliquées UMR CNRS 7641, Université de Versailles, 45 avenue des Etats-Unis, 78035, Versailles, France, Email: email@example.com
Publication date: October 2004