Title: Poincare Inequalities and Neumann Problems for the p(.) Laplacian

Abstract: In this talk, we discuss an established result proving an equivalence between weighted Poincare inequalities and the existence of weak solutions to a family of Neumann problems related to a degenerate p-Laplacian. We then extend this result to the variable exponent setting. We also explore a few of the adaptations required to prove this extension.