Difference between revisions of "PDE Geometric Analysis seminar"

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(Seminar Schedule Spring 2016)
(Tianling Jin)
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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.
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===Russell Schwab===
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Neumann homogenization via integro-differential methods
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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 09:25, 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.