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I am trying to solve an inverse problem based on variational principle. I will first present a forward problem that is already solved, and then present the inverse problem that I am trying currently ...

In Gelfand Calculus of Variation, chapter 1.7, the variational derivative is defined as: $$\left.\frac{\partial J}{\partial y}\right|_{x = x_0} = \lim_{\Delta\sigma \rightarrow 0}\frac{J[y+h]-J[y]}{\...

I would like to find an optimal probability density function (PDF) $f$. Given $b$, $$ \begin{array}{ll} \underset {f} {\text{minimize}} & C \\ \text{subject to} & 1 + \frac{b}{x} \displaystyle\...