"Geometric methods for two-dimensional water waves"
Time: 1:40 PM
Location: Hill 705
Abstract: We consider inviscid two-dimensional water waves.
Classical results
for the asymptotic behaviour at stagnation points are based on complex
analysis and transformation into singular integral equations. In this
lecture we will focus on new geometric methods which allow proving
generalised Stokes conjectures for non-simply-connected domains etc.
Part of the talk is the result of a collaboration with Eugen Varvaruca
(Imperial College London).
Tuesday, December 1st
Philippe G. LeFloch, University of Paris 6 and CNRS
" Einstein spacetimes with bounded curvature"
Time: 1:40 PM
Location: SERC 218
Abstract: In this lecture, I will present recent results on Einstein
spacetimes of general relativity, when the curvature is solely assumed to be
bounded and no assumption on its derivatives is made. One such result,
in a joint work with B.-L. Chen, concerns the optimal regularity of
pointed spacetimes in which, by definition, an ``observer'' has been
specified. Under geometric bounds on the curvature and injectivity
radius near the observer, there exist a CMC (constant mean curvature)
foliation as well as CMC--harmonic coordinates, which are defined in
geodesic balls with definite size depending only on the assumed
bounds, so that the components of the Lorentzian metric has optimal
regularity in these coordinates. The proof combines geometric
estimates (Jacobi field, comparison theorems) and quantitative
estimates for nonlinear elliptic equations with low regularity.
Wednesday, November 18th
Dr. Vittorio Martino, University of Bologna, Italy
"Periodic orbits of Reeb vector fields on an exotic $S^3$"
Time: 3:20 PM
Location: Hill 525
Tuesday, November 17th
Leonid Berlyand, Penn State University
" Homogenization in problems with non-separated scales and new elliptic inequality"
Time: 1:40 PM
Location: SERC 218
Abstract: The homogenization of PDEs with periodic or ergodic coefficients and
well separated scales is now well understood. In a joint work with H. Owhadi
(Caltech) we consider the most general case of arbitrary bounded coefficients.
Specifically, we study divergence-form scalar elliptic equations and vectorial
equations for elasticity with arbitrarily rough coefficients.
For these problems we establish two finite-dimensional approximations
of solutions, which we refer to as finite-dimensional homogenization
approximations:
. an approximation by a global basis with an explicit and optimal error
constant independent of the contrast and regularity of the coefficients.
. an approximation with a minimal amount of pre-computation with both
global and local bases.
Wednesday, November 11th
Special Nonlinear Analysis and PDEs
Sadok Kallel (NOTE: JOINT TOPOLOGY-NLA SEMINAR), Universite des Sciences et Technologies de Lille, France
" On the topology of Barycenter spaces and finite subset spaces"
Time: 3:20 PM
Location: Hill 525
Abstract:
Tuesday, November 10th
Sylvia Serfaty, University of Paris 6
" Lower bounds for two-scale energies and application to Ginzburg-Landau"
Time: 1:40 PM
Location: SERC 218
Abstract: I will describe joint work with Etienne Sandier in which we
derive from the Ginzburg-Landau energy of superconductivity a variational
problem for Abrikosov lattices (the vortex lattices arising in
superconductors) in a certain asymptotic regime. This energy is a
logarithmic-type interaction of points in the plane, and one expects it
achieves its minimum at the triangular lattice (of unit volume).
I will describe the method of the proof which is based on deriving lower
bounds for two-scale energies via the use of the ergodic theorem combined
with some kinds of Young measures on profiles.
Wednesday, October 28th
Special Nonlinear Analysis and PDEs
Luc Nguyen, Oxford University
" C^0 estimates for fully nonlinear Yamabe problems on locally conformally flat manifolds with umbilic boundary"
Time: 12:00 PM
Location: Hill 525
Abstract: In recent years, fully nonlinear versions of the Yamabe problem
have received much attention. In particular, for manifolds with boundary,
C^1 and C^2 a priori estimates have been proved for a large class of data under an additional
assumption
on C^0 bound. I will describe my joint work with Yanyan Li on C^0
estimates for such
problem when the background manifold is locally conformally flat and has
umbilic
boundary.
Tuesday, October 27th
Kyril Tintarev, Uppsala University
"Cocompact imbeddings: a functional-analytic view of concentration compactness"
Time: 1:40 PM
Location: SERC 218
Abstract: We discuss a notion of cocompact imbeddings relative to a group
of linear isometries and its connection to
the classical Brezis-Lieb lemma and to the concentration compactness
framework of P.-L. Lions.
As applications we present:
* A refined cocompactness property of critical Sobolev imbeddings.
* Existence of Talenti-type solutons for semilinear elliptic equations
with self-similar autonomous nonlinearities of critical growth.
* Cocompactness in the Trudinger-Moser inequality relative to M"obius
transformations and conformal dilations of the unit disk, and related refinements of the Trudinger-Moser
inequality.
We survey known cases of cocompact imbeddings, namely, Sobolev imbeddings
on cocompact manifolds, including
sub-Riemannian case, imbeddings of Sobolev spaces with fractional
exponents and imbeddings of Besov spaces.
Tuesday, October 20th
Xiaojing Xu, Beijing Normal University, China
"Existence and uniqueness of solutions for a class of non-Newtonian fluids with singularity and vacuum"
Time: 1:40 PM
Location: SERC 218
Abstract: The aims of this paper are to discuss existence and uniqueness
of local solutions for a class of non-Newtonian fluids with singularity
and vacuum
in one-dimensional bounded intervals. There are two important points in this
paper, one is that we allow the initial vacuum; another one is that the
viscosity term of momentum equation is with singularity.
Tuesday, October 13th
Jean Mawhin, Univ. of Louvain -la- Neuve, Belgium
"Some nonlinear problems involving mean curvature operators : Minkowskian versus Euclidean case"
Time: 1:40 PM
Location: SERC 218
Abstract: TBA
Tuesday, October 6th
Jiguang Bao, Beijing Normal University
" Necessary and sufficient conditions on solvability for Hessian inequalities"
Time: 1:40 PM
Location: SERC 218
Abstract: In this talk, we discuss the solvability of the Hessian inequality on the
entire space and provide a necessary and sufficient condition, which can
be regarded as a generalized Keller-Osserman condition. The similar results
to the other differential inequalities will also be introduced.
Tuesday, September 29th
Jinggang Tan, Universidad Tecnica Federico Santa Maria, Chile (NOTE: NEW ROOM)
"Positive Solutions of Nonlinear Problems Involving the Square Root of the Laplacian"
Time: 1:40 PM
Location: SERC 218
Abstract: We consider nonlinear elliptic problems involving a
nonlocal operator: the square root of the Laplacian in a bounded
domain with zero Dirichlet boundary conditions. We establish
the existence of positive solutions for problems with power non-
linearities in the subcritical case, Brezis-Nirenberg type existence
results for the critical problems under a small perturbation, non-
existence of positive solutions in some supercritical problems. We
also present the regularity and an $L^{infty}$ estimate of Brezis-Kato
type
for weak solutions, nonlinear Liouville type results, a priori esti-
mates of Gidas-Spruck type and a symmetry result of Gidas-Ni-
Nirenberg type.
This is joint work with Xavier Cabre.
Tuesday, September 22nd
Ovidiu Savin , Columbia University (NOTE: DIFFERENT ROOM)
"Parabolic Monge-Ampere equations"
Time: 1:40 PM
Location: Hill 552
Abstract: NOTE: DIFFERENT ROOM!!!!!!!!!!!!
In this talk we describe interior regularity of viscosity
solutions of certain parabolic Monge-Ampere equations. Equations of this
form appear in geometric evolution problems and in particular in the
motion of a convex $n$-dimensional hyper-surface embedded in $R^{n+1}$
under Gauss curvature flow.
This page was last updated on September 16, 2009 at 12:37 pm and is maintained by webmaster@math.rutgers.edu.
