ESI Senior Research Fellow Program, fall term 2003/04
Sobolev spaces with applications to PDE
Course of advanced graduate lectures by
Professor Vladimir Maz'ya
(Linköping University, Sweden)
Monday 14:00 - 16:00 and Tuesday 12:00 - 12:45, ESI lecture hall
starting on October 6, 2003
Contents: Sobolev spaces play an outstanding role in modern
analysis, in particular, in the theory of partial differential
equations and its applications in mathematical physics. They form an
indispensable tool in approximation theory, spectral theory,
differential geometry etc.. Needless to say the theory of these
spaces is of interest in itself being a beautiful domain of analysis.
I include the basics on Sobolev spaces, approximation and extension
theorems, imbeddings and compactness theorems, their connection with
isoperimetric inequalities, capacities with applications to Sobolev
spaces, Besov spaces, boundary traces of Sobolev functions, pointwise
inequalities for derivatives, Gagliardo-Nirenberg inequalities,
pointwise multipliers, variational approach to elliptic equations,
inequalities for general differential operators. Some open problems will
be formulated as well.
At the beginning of each lecture, I provide the students with copies
of its content. I distribute problems for my students which illustrate
my course and we discuss their solutions during 30 minutes each week.
I do not follow any textbook but a part of the material is borrowed
from the monographs
- V. Maz'ya "Sobolev Spaces", Springer, 1985
- V. Maz'ya, S. Poborchi "Differentiable Functions on Bad Domains",
World Scientific 1997
ESI Senior Research Fellow Program coordinated by Prof. Joachim
Schwermer, Institut für Mathematik, Universität Wien,
Strudlhofgasse 4, A-1090 Wien (Joachim.Schwermer@univie.ac.at).