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Universität Augsburg
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Universität Augsburg
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Dr. Manfred Sauter
Universität Ulm
spricht am
Donnerstag, 30. Juni 2016
um
16:30 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| The notion of the approximative trace allows to associate boundary traces to individual Sobolev functions in W^{1,p}(\Omega) on general open domains \Omega in R^d. It was introduced by Arendt and ter Elst to study the Dirichlet-to-Neumann operator on rough domains and draws from prior works by Maz'ya, Daners, Warma and Biegert, amongst others. If \Omega is Lipschitz, then the approximative trace agrees with the classical trace operator. For sufficiently irregular domains, however, the approximative trace exhibits a curious non-uniqueness phenomenon: the zero function in W^{1,p}(\Omega) can have a multitude of different approximative traces. In this talk we present novel geometric criteria for the uniqueness of the approximative trace. In particular, the approximative trace is unique on open sets with continuous boundary and on arbitrary connected domains in R^2. Furthermore, we provide an example that shows that the uniqueness of the approximative trace depends on p. These results answer several open questions. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. M. Peter |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).