As the title says, I need to find such a region. Taking any x, and any y1 and y2 I used the expression |F(x,y1) - F(x,y2)| and plugged in the function respectively for y1 and y2. Now I have to find values for x and y such that the following condition (Lipschitz condition) is satisfied: | 2x + (y1 + y2) | 0 (indeed after having simplified out the previous expression w.r.t the Lipschitz condition) My initial idea was to find x for which y = 0 and then the same thing for y1 and y2. This method though is not enough since for x = 0 the region of y1 and y2 for which the condition is satisfied, will have to depend on y1 and y2 directly. It will be better to attain a region such that it will not depend on the variables (obviously). I hope I am not incorrect here. I cannot seem to find a way to get this region and I would very much appreciate any insight given. Thank you.