PDE Geometric Analysis seminar: Difference between revisions
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u_t=|\nabla u|^{2-p} div(|\nabla u|^{p-2}\nabla u), | u_t=|\nabla u|^{2-p} div(|\nabla u|^{p-2}\nabla u), | ||
where 1<p<\infty. This equation arises from tug-of-war like stochastic games with white noise. It can also be considered as the parabolic p-Laplacian equation in non divergence form. This is joint work with Luis Silvestre. | where 1<p<\infty. This equation arises from tug-of-war like stochastic games with white noise. It can also be considered as the parabolic p-Laplacian equation in non divergence form. This is joint work with Luis Silvestre. | ||
===Russell Schwab=== | |||
Neumann homogenization via integro-differential methods | |||
In this talk I will describe how one can use integro-differential methods to attack some Neumann homogenization problems-- that is, describing the effective behavior of solutions to equations with highly oscillatory Neumann data. I will focus on the case of linear periodic equations with a singular drift, which includes (with some regularity assumptions) divergence equations with \emph{non-co-normal} oscillatory Neumann conditions. The analysis focuses on an induced integro-differential homogenization problem on the boundary of the domain. This is joint work with Nestor Guillen. | |||
Revision as of 15:25, 20 January 2016
The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.
Previous PDE/GA seminars
Tentative schedule for Fall 2016
Seminar Schedule Spring 2016
| date | speaker | title | host(s) |
|---|---|---|---|
| January 25 | Tianling Jin (HKUST and Caltech) | Holder gradient estimates for parabolic homogeneous p-Laplacian equations | Zlatos |
| February 1 | Russell Schwab (Michigan State University) | Neumann homogenization via integro-differential methods | Lin |
| February 8 | Jingrui Cheng (UW Madison) | ||
| February 15 | |||
| February 22 | Hong Zhang (Brown) | Kim | |
| February 29 | Aaron Yip (Purdue university) | TBD | Tran |
| March 7 | Hiroyoshi Mitake (Hiroshima university) | TBD | Tran |
| March 15 | Nestor Guillen (UMass Amherst) | TBA | Lin |
| March 21 (Spring Break) | |||
| March 28 | Ryan Denlinger (Courant Institute) | The propagation of chaos for a rarefied gas of hard spheres in vacuum | Lee |
| April 4 | |||
| April 11 | |||
| April 18 | |||
| April 25 | Moon-Jin Kang (UT-Austin) | Kim | |
| May 2 |
Abstracts
Tianling Jin
Holder gradient estimates for parabolic homogeneous p-Laplacian equations
We prove interior Holder estimates for the spatial gradient of viscosity solutions to the parabolic homogeneous p-Laplacian equation u_t=|\nabla u|^{2-p} div(|\nabla u|^{p-2}\nabla u), where 1<p<\infty. This equation arises from tug-of-war like stochastic games with white noise. It can also be considered as the parabolic p-Laplacian equation in non divergence form. This is joint work with Luis Silvestre.
Russell Schwab
Neumann homogenization via integro-differential methods
In this talk I will describe how one can use integro-differential methods to attack some Neumann homogenization problems-- that is, describing the effective behavior of solutions to equations with highly oscillatory Neumann data. I will focus on the case of linear periodic equations with a singular drift, which includes (with some regularity assumptions) divergence equations with \emph{non-co-normal} oscillatory Neumann conditions. The analysis focuses on an induced integro-differential homogenization problem on the boundary of the domain. This is joint work with Nestor Guillen.