Next Talk
Speaker: Dr. Sungjin Lee (Sogang University)
Title: Two-sided Gaussian estimates for fundamental solutions of second-order parabolic equations in non-divergence form
Date: Wednesday, May 6, 2026
Time: 16:30-17:30 (KST)
Zoom Link: https://us02web.zoom.us/my/repp.seminar (Meeting ID: 319 319 3319, PW: 112358)
Abstract: We construct the fundamental solution of second order parabolic operators P in non-divergence form under minimal assumptions, namely that the coefficients are of Dini mean oscillation in the spatial variables. We also establish that the fundamental solution satisfies a two-sided Gaussian estimate.
Specifically, we show that the upper and lower bounds follow from the local boundedness property and the weak Harnack inequality for the adjoint operator P^*, respectively. This provides a simpler and more direct proof of the Gaussian estimates when the coefficients have Dini mean oscillation in the spatial variables, avoiding the use of normalized adjoint solutions required in previous works.
Additionally, we study the regularity of parabolic operators P in non-divergence form and that of its adjoint operator P^*.
Later Talks
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)
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.