Talk #1
Speaker: Prof. Sun-Sig Byun (Seoul National University)
Title: Nonlinear Calderón-Zygmund Estimates for Parabolic Equations with Matrix Weights
Date: Tuesday, September 2, 2025
Time: 16:30-17:30 (KST)
Abstract: We investigate nonlinear parabolic equations whose coefficients act like matrix weights, distorting gradients in different directions rather than scaling them uniformly. Such anisotropic effects arise naturally in degenerate or heterogeneous media. Our main result is a Calderón-Zygmund type regularity result: whenever the forcing term has higher integrability, the solution’s gradient inherits the same improved integrability. This extends the classical weighted Calderón-Zygmund theory to a nonlinear, matrix-weighted framework.