Jiu-Yi Zhu

Bounds of singular sets for elliptic equations in $C^{1, Dini}$ domains with singular potentials

We study the quantitative codimension-two estimate for the singular set in the boundary neighborhoods of the solutions of \begin{equation*} \Delta u+V(x)u=0\qquad\text{in }\Omega, \qquad u=0\qquad\text{on }\partial\Omega, \end{equation*} where $\Omega\subset\mathbb R^n$ is a bounded $C^{1,\mathrm{Dini}}$ domain and $V\...