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Giles Auchmuty
Professor
of Mathematics
- University
of Houston
Office
Location:
PGH 696
Telephone:
(713) 743-3475
Fax:
(713) 743-3505
E-mail:
auchmuty@uh.edu
My
physical, and
mail, addresses
are
University of
Houston
Department of
Mathematics
4800 Calhoun Ave,
Houston, TX
77204-3008 |
Teaching:
In
Spring
2013,
I am
teaching Math 6367
Optimization
Theory and
Variational
Methods.
For
more information
about the
courses and a
listing of courses
taught in recent
years please
select the
Teaching
link above.
Research Interests:
My
research centers on
the mathematical
analysis of
elliptic boundary
value problems and
issues that arise in
classical field
theories - especially
electromagnetic and
gravitational fields.
Recent papers have
proved new results
about harmonic
functions and fields,
boundary values
(traces) of Sobolev
functions, the
existence and
properties of scalar
and vector potentials
and the well-posedness
of div-curl
systems that
arise in either
electromagnetic field
theory or in fluid
mechanics.
Many of these results
have involved either
elliptic spectral
theory, especially the
theory of Steklov
eigenproblems, or the
theory of Reproducing
Kernel Hilbert Spaces.
The results have often
depended on proving
new inequalities and
developing special
representation
results. Recently
I proved new
extensions of the
Sobolev imbedding
theorems for 3-d
fields where
integrability
conditions are imposed
on the Laplacian of a
potential - but not on
the function itself.
This is the
physical
situation for
gravitational and
electrostatic
potentials. With a
recent graduate
student Qi Han, we are
studying the
representation of
functions and fields
in exterior regions in
space and developing
well-posedness results
for elliptic
boundary value
problems on exterior
regions.
Another
continuing research
interest is in the
theory of potentials
for various classes of
3-dimensional vector
fields when various
types of boundary
conditions are
imposed.
This
research
is currently supported
by NSF award DMS
1108754 to study
"Steklov spectra and
Div-curl
analysis".
Maxwell's equations
are the most important
examples of div-curl
systems. See the link
to Research for more
information.
The work on these
issues is theoretical
mathematics, involving
functional analysis
and variational
principles. It
does not involve
computational
studies and I do
not have positions
available for
programmers.
Research Students:
Here is a
listing of
Ph.D. graduatets
whose theses I
supervised.
Currently
Manki Cho, Mauricio
Rivas and Liu
Puchen are working
on their doctoral
research with
me. I
have also supervised
many M.S. theses and
some undergraduate
honors students and
other research
projects. I
will be happy to
talk to students who
are interested in
possible research
projects and know
some mathematical
analysis.
Editorial:
This
section associated
with SIAM Review
welcomes unsolved
problems in applied
and applicable
mathematics.
Contributors should
send proposed problems
to Cecil C Rousseau.
If you can solve
posted problems please
let the proposer and
SIAM know about your
solutions.
Houston
Journal of
Mathematics.
The
Houston Journal of
Mathematics publishes
original research
results in many areas
of mathematics. See
their web-page Houston
J. of Mathematics
for details of the
submission process.
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