4 problems

Let $\Omega\subset\mathbb{R}^d$ be an open subset with smooth boundary. For $\lambda\in C^\infty(\overline{\Omega})$ with $\lambda>0$ on $\overline{\Omega}$, and…

Let $(V,\b5)$ be a weighted graph, let $o\in V$, and let $\sigma>1$. A nonnegative solution $u$ of the elliptic inequality … is a function on $V$ satisfying this inequality, where…

Let $M$ be an arbitrary complete connected Riemannian manifold, let $B(o,r)$ denote the geodesic ball centered at $o$, let $\mu$ be the Riemannian measure, let $G(x,o)$ be the Gree…

Let $M$ be an arbitrary complete connected Riemannian manifold, let $B(o,r)$ denote the geodesic ball of radius $r$ centered at $o$, let $cmu$ be the Riemannian measure, let $q$ be…