A new framework to solve rough nonlinear PDEs
调和分析及其应用专题报告
报告题目(Title)：A new framework to solve rough nonlinear PDEs
报告人(Speaker)：Sebastian Bechtel博士 (Université Paris-Saclay, France)
地点(Place)：后主楼1124
时间(Time)：2026年1月21日（周三）15:00-17:00
邀请人(Inviter)：杨大春
报告摘要
We will discuss a class of function spaces, called weighted Z-spaces, which characterise heat extensions of homogeneous Besov spaces. These spaces are well-suited to study the existence, regularity and uniqueness of weak solutions to rough non-linear PDEs. In this talk, I will give an overview about the non-linear strategy, thereby explaining where the specific properties of weighted Z-spaces come into action. This includes a notion of hypercontractive SIOs, which can meaningfully be investigated in weighted Z-spaces, as well as self-improving properties for weak solutions in weighted Z-spaces exploiting a new phenomenon of self-improving super-linear reverse Hölder inequalities.
