\int \int [ (\frac{\partial^{2} f(x)}{\partial x_{1}^{2}})^{2} + 2 (\frac{\partial^{2} f(x)}{\partial x_{1} \partial x_{2}})^{2} + (\frac{\partial^{2} f(x)}{\partial x_{2}^{2}})^{2}   ]dx_{1} dx_{2}