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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Sem. Równań Fiz. Mat.

 

Strong density in Sobolev spaces to manifolds


Prelegent: Antoine Detaille

2024-01-11 12:30

In striking contrast with what happens to classical Sobolev spaces, the space of smooth maps with values into a compact manifold $N$ does not need to be dense in the space of $N$-valued $W^{s,p}$ maps.
In this talk, I will review the history of this problem, culminating with Bethuel's theorem for $W^{1,p}$ and its extensions to $W^{s,p}$, which gives a necessary and sufficient condition on the topology of the target manifold $N$ in order to smooth maps to be dense as well as a suitable class of almost smooth maps that is always dense.
I will finish with a new result about an improved dense class in Sobolev spaces to manifolds.