3 problems

Let $f: [-1,1]^d \to \mathbb{R}$, and let $u$ solve the continuum biharmonic problem … Assume either that $u\in C^5((-1,1)^d)$ with $\|u\|_{C^5((-1,1)^d)}\leq C<\infty$, or that…

Let $n=2$ or $n=3$, let $V_N$ denote the finite domain of the membrane model, let $\psi=(\psi_x)_{x\in V_N}$ be its field, let $\operatorname{E}_N$ denote expectation, and let…

Exponential decay conjecture. The covariances of the membrane model decay exponentially in the distance in the critical and supercritical dimensions: there should exist $c,c'>0$ su…