# 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 2019-Spring 2020

## PDE GA Seminar Schedule Fall 2018-Spring 2019

date | speaker | title | host(s) |
---|---|---|---|

August 31 (FRIDAY), | Julian Lopez-Gomez (Complutense University of Madrid) | The theorem of characterization of the Strong Maximum Principle | Rabinowitz |

September 10, | Hiroyoshi Mitake (University of Tokyo) | On approximation of time-fractional fully nonlinear equations | Tran |

September 17, | Changyou Wang (Purdue) | Some recent results on mathematical analysis of Ericksen-Leslie System | Tran |

September 24/26, | Gunther Uhlmann (UWash) | TBA | Li |

October 1, | Matthew Schrecker (UW) | TBA | Kim and Tran |

October 8, | Anna Mazzucato (PSU) | TBA | Li and Kim |

October 15, | Lei Wu (Lehigh) | TBA | Kim |

October 22, | Annalaura Stingo (UCD) | TBA | Mihaela Ifrim |

Time: TBD, | Jessica Lin (McGill University) | TBA | Tran |

November 5, | Albert Ai (University of Berkeley) | TBA | Mihaela Ifrim |

December 10, | ( ) | TBA | |

January 28, | ( ) | TBA | |

March 4 | Vladimir Sverak (Minnesota) | TBA(Wasow lecture) | Kim |

March 18, | Spring recess (Mar 16-24, 2019) | ||

April 29, | ( ) | TBA |

## Abstracts

### Julian Lopez-Gomez

Title: The theorem of characterization of the Strong Maximum Principle

Abstract: The main goal of this talk is to discuss the classical (well known) versions of the strong maximum principle of Hopf and Oleinik, as well as the generalized maximum principle of Protter and Weinberger. These results serve as steps towards the theorem of characterization of the strong maximum principle of the speaker, Molina-Meyer and Amann, which substantially generalizes a popular result of Berestycki, Nirenberg and Varadhan.

### Hiroyoshi Mitake

Title: On approximation of time-fractional fully nonlinear equations

Abstract: Fractional calculus has been studied extensively these years in wide fields. In this talk, we consider time-fractional fully nonlinear equations. Giga-Namba (2017) recently has established the well-posedness (i.e., existence/uniqueness) of viscosity solutions to this equation. We introduce a natural approximation in terms of elliptic theory and prove the convergence. The talk is based on the joint work with Y. Giga (Univ. of Tokyo) and Q. Liu (Fukuoka Univ.)

### Changyou Wang

Title: Some recent results on mathematical analysis of Ericksen-Leslie System

Abstract: The Ericksen-Leslie system is the governing equation that describes the hydrodynamic evolution of nematic liquid crystal materials, first introduced by J. Ericksen and F. Leslie back in 1960's. It is a coupling system between the underlying fluid velocity field and the macroscopic average orientation field of the nematic liquid crystal molecules. Mathematically, this system couples the Navier-Stokes equation and the harmonic heat flow into the unit sphere. It is very challenging to analyze such a system by establishing the existence, uniqueness, and (partial) regularity of global (weak/large) solutions, with many basic questions to be further exploited. In this talk, I will report some results we obtained from the last few years.