Abstract: Consider the weak solution $u$ to the elliptic equation $\mathcal{L}(u)=\partial_{i}(a^{ij}(x)\partial_{j}u)+b^{i}(x)\partial_{i}u+c(x)u=0$. There has been extensive study about the singular set $\{u(x)=\nabla u(x)=0\}$ for the equation with weakly regular coefficients. In this talk, I will discuss the recent progress about the volume estimates for singular sets with $a^{ij}$ assumed only to be H\"older continuous. It is sharp as it is the weakest condition in order to define the singular set of $u$ according to elliptic estimates. This talk is based on joint work with Wenshuai Jiang.

Bio-Sketch: Yiqi Huang is currently a graduate student at MIT under the supervision of Toby Colding. He is interested in differential geometry and geometric PDEs.

Zoom: https://us02web.zoom.us/j/81975816692?pwd=SGhSN01Sd2l1dGpDbjAxZzFKRUpNQT09                                                                                Meeting ID: 819 7581 6692   Passcode: 254959