Weighted Poincare' Inequalities for Solutions to A-Harmonic Equations

Shusen Ding, Craig A. Nolder

We first prove a local $A_r$-weighted Poincar\'e inequalities for solutions to $A$-harmonic equations of the form: $d^{\star} A(x, d \omega) =B(x,d\omega)$. Then, as an application of the local result, we prove a global $A_r$-weighted Poincar\'e inequality for functions that are solutions to the such equations in John domains.