Next Talk
Speaker: Prof. Kyungkeun Kang (Yonsei University)
Title: Weak Solutions to Nonlinear Diffusion Equations with Drift and Applications
Date: Wednesday, October 29, 2025
Time: 16:30-17:30 (KST)
Zoom Link: https://us02web.zoom.us/my/repp.seminar (Meeting ID: 319 319 3319, PW: 112358)
Abstract: We study weak solutions to the porous medium and fast diffusion equations with drift terms, where the drift satisfies a scaling-invariant condition governed by its L^q-norm. As applications, we revisit a range of nonlinear diffusion systems, providing refined and extended results on the existence and regularity of solutions. In a recent development, we establish the existence of non-negative weak solutions with sharp gradient estimates, even in the presence of measure-valued external forces.
Later Talks
Speaker: Dr. Kyeong Song (Korea Institute for Advanced Study)
Title: Gradient estimates for elliptic measure data problems with double phase
Date: Tuesday, November 11, 2025
Time: 16:30-17:30 (KST)
Abstract: We establish local Calderón-Zygmund type gradient estimates for a class of nonlinear measure data problems whose leading operator switches between two different kinds of degenerate elliptic phases. Our proof is based on new comparison estimates and regularity estimates for reference problems below the energy range. We also identify new and natural structural assumptions for our results.