2 problems

Let $N=4$ and let $\Omega$ be $\mathbb{R}^{4}$, $\mathbb{T}^{4}$, or a bounded $C^{2}$ Neumann domain. Let $\mathcal{A}_M(\Omega)$ denote the admissible class of densities of mass…

Let $\Omega=B_R(0)\subset\mathbb{R}^2$ with $R>0$ and $k>0$. A steady state is a solution $(u,v)$ of the stationary problem considered in the paper, with prescribed mass…