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Universität Augsburg
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Universität Augsburg
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Dr. Stefan Schiffer
MPI Leipzig
spricht am
Donnerstag, 27. Juni 2024
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15:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
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Various results on regularity theory of differential equations or inequalities involving differential operators (Korn, Poincaré...) may be shown on the full space by employing different techniques, for instance Fourier analysis. These techniques are, however, not always available on bounded domains; hence proving such results on domains often is more challenging. A standard approach is to extend the function in question to the full space and use the results available there to prove it for the domain.
In this talk, I will discuss a specific extension theorem for divergence-free functions and some of its applications. In more detail, the central question may be posed as follows: For which domains can we find a linear and bounded extension operator that maps $L^p$ into $L^p$ and preserves the constraint ${\rm div} u =0$? Even for quite simple domains such an extension naturally is challenging in the end-point cases $p=1$ and $p=\infty$. We discuss the case of Lipschitz bounded sets and the exponent $p$ belonging to those endpoint cases where we can answer above question in the affirmative. This talk is based on joint work with F. Gmeineder (U Konstanz). |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Lisa Beck |