[CvGmt News] seminari Schurich e Mantegazza 16/3
Daniele Castorina
castorin at mat.uniroma2.it
Wed Apr 10 11:08:55 CEST 2013
Cari amici,
vi segnalo il prossimo _doppio_ seminario di ED a Tor Vergata:
Martedi' 16 Aprile 2013, h 14:30, Aula Dal Passo
Friedemann Schuricht - Università di Dresda
Eigenvalue problem of the 1-Laplace operator.
The eigenvalue problem of the $p$-Laplace operator is extensively
studied for $p>1$. We are interested in the highly degenerated limit
case $p=1$ where some new phenomena can be observed. First, the
formal eigenvalue equation is not well defined and one has to
clarify what an eigensolution of the $1$-Laplace operator should be.
Then the existence of a sequence of eigensolutions can be shown.
Since the corresponding eigenvalue equation has too many solutions,
a further equation satisfied by eigensolutions is derived.
Martedi' 16 Aprile 2013, h 15:30, Aula Dal Passo
Carlo Mantegazza - Scuola Normale Superiore di Pisa
Evolution by curvature of a triod in the plane (Joint work with
Matteo Novaga and Annibale Magni).
We consider the motion by curvature of a network of three smooth
embedded curves in a convex subset of the plane, connected through a
triple junction (a triod) and with fixed endpoints on the boundary.
Such a flow represents the evolution of a two-dimensional 3-phase
system where the energy is simply the sum of the lengths of the
interfaces, moreover, this is the simplest example of curvature flow
of a set which is ``essentially'' non regular. We prove that the
flow exists smooth until the lengths of the three curves stay far
from zero. If this is the case for all times, then the network
converges to the Steiner minimal connection between the three
endpoints. Finally, we discuss some other recent results and the
possible generalizations to higher dimensions.
------------------------------------------------------------------------
--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: castorin at mat.uniroma2.it
tel: +390672594653
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