Global poincaré inequalities for green's operator applied to the solutions of the nonhomogeneous A-harmonic equation

AbstractBoth local and global Ar-weighted Poincaré inequalities for Green's operator applied to the solutions of the nonhomogeneous A-harmonic equation in John domains are established. As applications of the Poincaré inequalities for Green's operator, the Ar-weighted Sobolev imbedding inequalities for Green's operator in John domains are also proved