I know that a Jeffreys prior is the information maximizing distribution for the statistical channel. However, I want to know if I define mutual information as $$I(x;y)=h(x)-h(x|y)$$ where $h(.)$ is differential entropy and $x$ and $y$ are continuous random variables. If I use $p(x)$ the PDF of $x$ to be the Jeffrey prior. Does $$h(x)=-\int p(x)log_2 p(x) dx$$ maximizes the $I(x;y)$?