Howdy, today, we study a simple invariant concerning the Monge-Ampère equations. Let us consider the following simple case
in , where . For a beginner, we refer to an entry from wikipedia [here].
We now look for a function of the form
where is a constant to be determined. A quick calculation shows that
Therefore, is chosen so that . Hence
is also a solution. This property can be found in a paper by Kutev [here].