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Variational convergence of EVI-gradient flows in metric spaces.

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Speaker: 
Giuseppe Savaré
Affiliation: 
Università di Pavia
Date: 
Mon, 2017-09-11 09:30 - 10:30
Location: 
MPIM Lecture Hall

It is well known that gradient flows of convex and lower semicontinuous functionals $(\phi^h)_{h\in \mathbb N}$ in a Hilbert space are stable with respect to Mosco-convergence (i.e.~$\Gamma$-convergence with respect to the strong and the weak topology) of the driving functionals $\phi^h$.

In general metric spaces the situation is more delicate, due to lack of a weak topology and of the corresponding compactness properties. Moreover, the existence of a contracting semigroup generated by a (geodesically) convex functional also depends on the properties of the distance function.

We will show that for gradient flows characterized by a family of evolution variational inequalities (EVI-flows), a good stability property is in fact equivalent to a reinforced notion of $\Gamma$-convergence, which does not require any equi-compactness of the sublevels of the functional.

 

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