1. The problem statement, all variables and given/known data f(x,y) is a two variables function for which the hypothesis of Schwarz's theorem hold in a point (a,b). is f continuous in (a,b)? 3. The attempt at a solution I think it is, because being the two mixed partials continuous in (a,b) the function is twice differentiable, and therefore globally Lipschitz, which implies continuity. Am I right?