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Mathematisches Kolloquium

  • Prof. Dr. Irene Benedetti (Universita degli Studi di Perugia)

"Nonlocal multivalued problems in abstract spaces"
Abstract: The interest for multivalued equations in abstract spaces is motivated by the study of control problems for partial differential equations. Moreover, nonlocal boundary conditions, such as mean value and multi-point conditions, are particularly suitable to model problems arising in physics. The existence of solutions for these problems is frequently studied with topological techniques based on fixed point theorems for a suitable solution operator. This requires strong compactness conditions, which are very hard to check in an infinite dimensional framework. In this talk will be presented three approaches that weaken the compactness conditions usually required.
A first technique is based on the concept of measure of non-compactness combined with a topological degree theory. Alternatively, weak topologies can be exploited, joined with the classical Ky Fan Fixed Point Theorem. Finally, one can consider the multivalued problems in a Hilbert space compactly embedded into a Banach space, in connection with Hartmann-type conditions. Several examples of partial differential equations applying the described three approaches will be shown.

PD Dr. Väth lädt um 10:45 Uhr zum Kaffeetrinken in Raum 129 ein.
3. März 2015, 11:15 Uhr, HS 228 (Ulmenstraße 69, Haus 3)
Kolloquiumsleiter: PD Dr. Martin Väth

  • Prof. Dr. Andrew Wood (University of Nottingham)

"Kent distributions on Stiefel Manifolds"
Abstract: The von Mises-Fisher distribution on the unit sphere is a widely used statistical model for observations on the unit sphere.  A limitation in many applications is that it can not model depatures from rotational symmetry about the mean direction.  Kent (1982) proposed a 5-parameter distribution on the unit sphere in R^3 which includes the von Mises-Fisher distribution as a subfamily and has ellipse-like contours of constant density.  After reviewing relevant distributions on the unit sphere, the talk will discuss the analogous problem on Stiefel manifolds and explain how similar ideas can be used to construct Kent-like distributions in this setting.
12.02.2015, 11:00 Uhr, HS 125 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Wolf - Dieter Richter

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