All Questions

I am trying to compute the first variation of the functional $$\mathcal F(\rho) = \int_{\Omega} R(x;\rho) d\rho(x)$$ where $R$ is some function of $x$ that also depends on $\rho$. Here $\rho$ is a ...

I want to minimize the functional $$ F=\int{L(u)}dx, $$ where $L= u_x^2-u^2$ is the Lagrangian function of the functional. Even if its Euler-Lagrange equation is easily found and solved, I want to try ...

First of all, I am sorry for such naivety. I have not all the intuition in hard analysis as I wish. I am studying Perelman's work and his big first contribution is to prove that the Ricci flow is in ...

For a convex lower-semicontinuous functional on a Hilbert space $I\colon H\rightarrow\mathbb{R}$, it is shown in Evans' PDE that the Hilbert-space-valued ODE $$\begin{cases}\mathbf{u}'(t)\in-\partial ...