Symmetry of second derivatives
Mathematical theorem / From Wikipedia, the free encyclopedia
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In mathematics, the symmetry of second derivatives (also called the equality of mixed partials) refers to the possibility of interchanging the order of taking partial derivatives of a function
of variables without changing the result under certain conditions (see below). The symmetry is the assertion that the second-order partial derivatives satisfy the identity
so that they form an symmetric matrix, known as the function's Hessian matrix. Sufficient conditions for the above symmetry to hold are established by a result known as Schwarz's theorem, Clairaut's theorem, or Young's theorem.[1][2]
In the context of partial differential equations it is called the Schwarz integrability condition.