Generalized Poincar´e Inequalities for Solutions to the A-Harmonic Equation in Certain Domains

We first prove local versions of the Poincar´e inequality for solutions to the A-harmonic equation. Then, as applications of the local results, we obtain the global versions of the Poincar´e inequality for solutions to the A-harmonic equation in LsŽ , 0.-averaging domains and Ls-averaging domains, respectively. These results can be considered as generalizations of the classical Poincar´e theorem.