  Generated Jacobian equations are Monge-Amp\`ere type equations which contain
optimal transport as a special case. Therefore, optimal transport case has its
own special structure which is not necessarily true for more general generated
Jacobian equations. Hence the theory for optimal transport can not be directly
transplanted to generated Jacobian equations. In this paper, we point out the
difficulties that prevent applying the proof the local H\"older regularity of
solutions of optimal transport problem from \cite{Loeper2009OnTR} directly to
Generated Jacobian Equations, we then discuss how to handle these difficulties,
and prove local H\"older regularity in the generated Jacobian equation case.
