7 problems

Let $\varphi:\bD\to\bC$ be analytic and injective, where $\bD$ is the unit disk and $\bT$ its boundary circle. Anderson's conjecture. There exists $\zeta\in\bT$ such that … The con…

Let $\Omega$ be a bounded Jordan domain with a Hölder-$C^1$ corner of opening $\pi\alpha$ at $z_0\in\partial\Omega$, where $0<\alpha\leq 2$. Let $\mu$ be a non-negative measure wit…

Let $\Omega$ be a bounded open Lipschitz set satisfying an exterior sphere condition, let $k\in\mathbb{N}$ be fixed, and let $h_k\in C_0(\Omega)$ satisfy $|\varphi_{k,s}|\leq h_k$…

Let $\Omega$ be the bounded Euclidean domain under consideration, let $e_\lambda$ be an eigenfunction of the fractional Laplacian, and consider global $L^p(\Omega)$ bounds. Boundar…

Let $\Omega\subset\mathbb{R}^n$ be a bounded domain, let $V\in L^1_{\mathrm{loc}}(\Omega)$ be a subcritical potential, and let $\phi_1$ be a generalized first eigenfunction for the…

Let $D$ be a domain and let … should extend to all points of $\partial D$, including irregular boundary points. This would complete the boundary scope of the paper's heat-kernel es…

Let $D$ be a domain, let $p_D(t,x,y)$ denote the transition density of the fractional Laplacian killed upon exiting $D$, and let $\tau_D$ be the first exit time from $D$. For certa…