Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. From my knowledge of math, I know that one sufficient condition for the Hessian matrix to be symmetric(or resp. Continuity of the second order partial derivatives [at an interior point] is a sufficient (but not necessary) condition for the existence of the second derivative, and thus by transitivity for the symmetry of the Hesse matrix.


This seminar was presented to show the results of my research on magnetic thin films for my Licentiate diploma in Physics Engineering.
Continuity of the second partial derivatives is a strong condition that implies for example the symmetry of the Hesse matrix. Continuity of the partial derivatives is easier to check, and most of the functions one actually encounters have either that, or aren't twice differentiable, so the more general criterion is in practice rarely needed.


Continuity of the second order partial derivatives is a sufficient (but not necessary) condition for the existence of the second derivative.



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