Research Group:
Speaker:
Francesco Nobili
Institution:
SISSA
Schedule:
Friday, July 3, 2020 - 15:00
Location:
Online
Location:
Zoom (sign in to get the link)
Abstract:
The dependence on $p$ of $p$-weak gradients is a classical problem in the Analysis of Metric Measure Spaces. In this seminar, we review the literature concerning the definition of Sobolev Spaces $W^{1,p}(X)$ on a metric measure space $X$ from a didactic point of view and discuss the dependence of $|\nabla f|_p$ in the framework of 'weak upper gradients'. Moreover, we exhibit an example of $X$ where $p$-weak upper gradients may depend on $p$. Finally, if time permits, we conclude the presentation by showing that the class of metric measure spaces having synthetic Ricci lower bounds enjoys the property of independence of $p$-weak upper gradients.