Abstract for the talk on 18.02.2022 (14:00 h)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Gael Diebou Yomgne (Universität Bonn)
Nonlinear elliptic PDEs subject to irregular data
In this talk, I will discuss a new approach to the solvability
of semilinear elliptic problems (in bounded and unbounded domains)
supplemented by data assuming low regularity. The method exploits the
nature of the nonlinearity as well as other intrinsic properties of the
equation to select suitable functional frameworks where solutions are
sought for. In the process, we borrow tools from modern harmonic analysis
and function spaces theory.
Two equations of interest will be mentioned: The weakly harmonic map
problem and the stationary Navier-Stokes flow. I also plan to comment on
the parabolic theory if time allows.