Difference between revisions of "PDE Geometric Analysis seminar"
Line 25: | Line 25: | ||
|Changyou Wang (U. of Kentucky) | |Changyou Wang (U. of Kentucky) | ||
|[[#Changyou Wang (U. of Kentucky)| | |[[#Changyou Wang (U. of Kentucky)| | ||
− | '' | + | ''Phase transition for higher dimensional wells'']] |
|Misha | |Misha | ||
|- | |- | ||
Line 69: | Line 69: | ||
===Changyou Wang (U. of Kentucky)=== | ===Changyou Wang (U. of Kentucky)=== | ||
− | '' | + | ''Phase transition for higher dimensional wells'' |
+ | |||
+ | Abstract. For a potential function $F$ that has two global minimum sets consisting of two compact connected | ||
+ | Riemannian submanifolds in $R^k$, we consider the singular perturbation problem: | ||
+ | |||
+ | Minimizing $\int (|\nabla u|^2+\frac{1}{\epsilon2} F(u))$ under given Dirichlet boundary data. | ||
+ | |||
+ | I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter $\epsilon$ | ||
+ | tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and | ||
+ | the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary | ||
+ | data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem. | ||
===Philippe LeFloch (Paris VI)=== | ===Philippe LeFloch (Paris VI)=== |
Revision as of 09:26, 17 September 2010
Contents
PDE and Geometric Analysis Seminar - Fall 2010
The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm
Seminar Schedule
date | speaker | title | host(s) |
---|---|---|---|
Sept 13 | Fausto Ferrari (Bologna) |
Semilinear PDEs and some symmetry properties of stable solutions |
Misha |
Sept 27 | Arshak Petrosyan (Purdue) | Misha | |
Oct 7, Thursday, 4 pm, Room: TBA. Special day, time & room. | Changyou Wang (U. of Kentucky) | Misha | |
Oct 11 | Philippe LeFloch (Paris VI) | Misha | |
Oct 29 Friday | Irina Mitrea (IMA & U of Virginia) | WiMaW | |
Nov 8 | Maria Gualdani (UT Austin) | Misha | |
Date TBA | Mikhail Feldman (UW Madison) | TBA | Local speaker |
Date TBA | Sigurd Angenent (UW Madison) | TBA | Local speaker |
Abstracts
Fausto Ferrari (Bologna)
Semilinear PDEs and some symmetry properties of stable solutions
I will deal with stable solutions of semilinear elliptic PDE's and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.
Arshak Petrosyan (Purdue)
TBA
Changyou Wang (U. of Kentucky)
Phase transition for higher dimensional wells
Abstract. For a potential function $F$ that has two global minimum sets consisting of two compact connected Riemannian submanifolds in $R^k$, we consider the singular perturbation problem:
Minimizing $\int (|\nabla u|^2+\frac{1}{\epsilon2} F(u))$ under given Dirichlet boundary data.
I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter $\epsilon$ tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.
Philippe LeFloch (Paris VI)
TBA
Irina Mitrea
TBA
Maria Gualdani (UT Austin)
TBA