I'm studying Sobolev spaces these days and came across a property of Poincare Inequality for mean-zero functions that I don't understand;
$u(x,y)=-u(x,-y) \implies \int_\Omega u=0$ and that Poincare Inequality for zero mean-value functions can be applied
The domain is $\Omega=B(0,1) \subset \Bbb{R^2}$. Can anyone guide me on what I'm missing here?