Ett informationsblad från matematiska institutionen vid Linköpings universitet. Material till Lite Mat lämnas till Maud Lindström litemat@mai.liu.se senast torsdagar kl 12.00.

Vi har dessutom ett arkiv av gamla nummer.

***LITE MAT***

Ett informationsblad från matematiska institutionen vid Linköpings universitet

v25 2003

Matematiska kollokviet

Onsdagen den 25 juni, kl. 13.00-14.00 talar Prof. Nageswari Shanmugalingam, Cincinnati,

Banach space valued Newton-Sobolev spaces on metric measure spaces

Sammanfattning: Sobolev spaces have been an integral part of the study of PDEs and quasiconformal mappings between Euclidean spaces. Recent surge of interest in the study of quasiconformal mappings between domains in metric measure spaces indicates the desirability of constructing Sobolev type spaces of functions between metric spaces.

Given that general metric spaces need not have a group structure, spaces of functions between two metric spaces in general need not have a vector space structure. We can however compensate for this by embedding the target metric space isometrically into a Banach space, for example, into , and the corresponding space of functions inherit the vector space structure.

In this talk, we will construct an analogue of Sobolev spaces, called Newtonian spaces, of functions from a metric measure space into a fixed Banach space. To do so, we will use the notion of upper gradients first developed by Heinonen and Koskela. We will discuss some elementary properties of this function space, and discuss the independence of Poincaré inequalities from the target Banach space. In particular, we will prove that Newtonian functions from the given metric space X into any

Banach space satisfy a Poincaré inequality if and only if real-valued Newtonian functions from X satisfy a Poincaré inequality.

We will also discuss how to extract the class of Newtonian functions from X to a given metric space Y from the Newtonian space of functions from X to a Banach space into which Y was embedded.

This talk is based on joint work with Heinonen, Koskela, and Tyson (2001).

Välkomna!
Anders Björn

Doktorandkurser Tillämpad matematik

Läsåret 2003-2004 ges följande doktorandkurser vid TM:

Höstterminen 2003
Grafteori, 5p (Leif Melkersson)
Integrationsteori, 5p (Bengt Ove Turesson)
Topologisk kombinatorik, 5p (Svante Linusson) (november-mars)

Vårterminen 2004
Algebra, 5-10p (Leif Melkersson)
Funktionalanalys, 5p (Björn Textorius)
Operatorteori, 5p (Anders Björn)

Detaljerad information om kurserna kommer senare.

Välkomna!
Svante Linusson
Bengt Ove Turesson

Lite Mat gör nu sommaruppehåll och återkommer vecka 33.

GLAD SOMMAR!!!

Mer information om MAI finns på under MAIs hemsida
Material till Lite Mat lämnas till Maud Lindström senast torsdagar kl 12.00.
Tel 013-281405, Fax 013-100746, Email: litemat@mai.liu.se

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