  The Poincare Inequality is an extremely useful tool in the analysis of PDEs.
A significant amount of literature has dealt with finding the optimal constant
$C(p,\Omega)$, depending only the domain $\Omega$, and the $L^p$ norm in
question. For convex subsets $\Omega\subset \mathbb{R}^n$, an optimal constant
is known. There has also been some work done for $\textit{specific}$ non-convex
subsets. For a general open, bounded subset, finding the optimal constant is a
non-trivial task. This paper will outline a method for finding a non-trivial
estimate for $C$ when $\Omega\subset \mathbb{R}^n$ is non-convex, by first
observing $\Omega\subset \mathbb{R}^n$ has finite Lebesgue measure, and using
local estimates on subsets of $\Omega$ to obtain a global estimate on $\Omega$.
