# PDE Geometric Analysis seminar

The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.

## Contents

### 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) | Tran & Kim | |

February 15 | Paul Rabinowitz (UW Madison) | Tran & Kim | |

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 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.