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Universität Augsburg
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Universität Augsburg
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Professor Dr. Andrea Braides
Università di Roma
spricht am
Donnerstag, 15. Januar 2026
um
15:45 Uhr
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TUM, Boltzmann-3, Garching, Raum 03.08.011, Etage 3
über das Thema:
| Abstract: |
| We study the asymptotic behaviour of Gagliardo $H^s$ seminorms on thin films of thickness tending to 0. We show that the behaviour is different in the low-integrability regime ($s<1/2$) and in the high-integrability regime ($s>1/2$). In both cases, there exists a critical scaling (depending on s) for which the limit is dimensionally reduced. In the case $s>1/2$ the scaling highlights a combined effect of the geometrical dimensions and the relevant range of interactions in the Gagliardo seminorms, and the limit is a $H^1$ seminorm. Moreover, in the light of the results by Bourgain, Brezis and Mironescu (BBM) and Maz'ya and Shaposhnikova (MS), we study the asymptotic behaviour as $s\to 1$ and $s\to 0$. In the case $s\to 1$ the asymptotic behaviour highlights a separation of scales and a compatibility with the BBM result. In the case $s\to 0$ the scaling is purely geometrical and leads to a $H^{1/2}$ seminorm, differently from the MS result. The analysis relies on two different approaches to compactness. Work in collaboration with A. Pinamonti and M. Solci, |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Gero Friesecke |