5 problems

Let $\Omega\subset\mathbb{R}^2$ be a Jordan domain, and let $\partial\Omega$ denote its boundary. For $x\in\partial\Omega$, let $\varepsilon(x,r)$ be the Carleson $\varepsilon$-fun…

Let $\Omega\subset\mathbb R^n$ be a one-sided NTA domain whose Green function with some pole $p$ satisfies, for some $\delta>0$ and constants $c_1,c_2>0$, bounds of the form … for…

Let $n=2$. Let $\Omega$ be a one-sided NTA domain, and let $u$ and $v$ be as above, with $u/v$ agreeing on $B(z,r)\cap\partial\Omega$ with a real-analytic function $R$. Assume more…

Let $\Omega$ be a one-sided NTA domain, and let $u$ and $v$ be positive harmonic functions as above, vanishing on the relevant portion of the boundary, such that their quotient agr…

Let $D$ be a domain, let $t\in\mathbb R$, and let $\rho^D(t,\mathord\cdot)$ denote the density from Theorem 2.7. Boundary regularity conjecture. For each $t\in\mathbb R$, the funct…