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The problem of (in)dependence on p of weak gradients

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. 

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