4 problems

Classification conjecture for Serrin bands. Any Serrin band in $\mathbb{R}^2$ is, up to similarity, one of the periodic bands $\Omega_\tau$, with $\tau\in(0,1]$.

Let $u$ solve the torsion problem on a domain $\Omega$ with boundary $\Gamma$, and let $u_\nu$ denote its normal derivative on $\Gamma$. Quantitative Serrin stability bounds measur…

Let $\Omega\subseteq\mathbb{S}^{n+1}$ be a domain with smooth connected boundary. Suppose there is a positive function $u\in C^2(\overline{\Omega})$ and a function…

Let $u$ solve … where $Omega$ is a bounded domain in $\mathbb{R}^N$ with boundary $Gamma$ of class $C^{2,tau}$, $0<tau<1$, and $f$ is locally Lipschitz continuous. Let $r_e$ and…