Next Talk
Speaker: Dr. Wontae Kim (Korea Institute for Advanced Study)
Title: Calderón-Zygmund type estimates for the parabolic double phase system
Date: Wednesday, May 20, 2026
Time: 16:30-17:30 (KST)
Zoom Link: https://us02web.zoom.us/my/repp.seminar (Meeting ID: 319 319 3319, PW: 112358)
Abstract: In this talk, we discuss Calderón-Zygmund type estimates for the parabolic double phase system. We provide a phase analysis adapted to the desired estimates. A new feature of our approach involves estimating the radius of each cylinder in the Calderón-Zygmund decomposition, which is crucial for obtaining suitable comparison estimates and determining the optimal range of q. Furthermore, despite the non-standard growth conditions inherent in the system structure, it possesses scaling invariant properties within each intrinsic cylinder, as identified through our phase analysis.
Later Talks
Speaker: Prof. Sunghan Kim (Uppsala University)
Title: Regularity of thin constraint maps
Date: Wednesday, June 3, 2026
Time: 16:30-17:30 (KST)
Abstract: Thin constraint maps are energy-minimizing maps subject to an image constraint imposed on a thin space inside the domain. A natural example is the Signorini problem, and they also arise from the Caffarelli-Silvestre extension for nonlocal constraint maps. This problem has also been studied as a free boundary problem for harmonic maps into manifolds-with-boundary. Analogous to the thick case, thin constraint maps develop free boundaries due to the presence of the thin obstacle, and also developing discontinuities, often for topological reasons. While the partial regularity theory of these maps was established in the nineties, little has been known concerning their free boundaries. In this talk, I will present a new result for thin constraint maps concerning the full regularity in a uniform neighborhood of their non-coincidence set, even for slightly nonconvex thin obstacles. This result is surprisingly stronger than that of the thick obstacle case, where discontinuities appear on the free boundary even for convex obstacles. My talk will be based on joint work with Marvin Weidner (University of Bonn) and Hui Yu (National University of Singapore).