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Writer's pictureQuoc-Hung Nguyen

IMS Lecture Series on Regularity Theory for Quasilinear Equations

Updated: Oct 20, 2021


Organizer: Quoc-Hung Nguyen, Institute of Mathematical Sciences, ShanghaiTech University, Shanghai, China.


The goal of the lecture series is to bring together leading experts and young researchers to discuss recent developments in regularity theory for quasilinear equations. The Lectures will take place via Zoom.


Click here to see: the poster for the workshop


How to use Zoom

  • The seminar will take place over Zoom. Please download and setup Zoom via link: https://zoom.us/download

  • Please log in with your real name.


Program:

1. May 1st, 2020


  • 9 pm Beijing Time (GMT+8):


Speaker: Giuseppe Mingione, University of Parma, Italy.


Title: Gradient estimates from uniformly to non-uniformly elliptic problems, Part 1


Abstract: I will give an overview of pointwise gradient estimates for solutions to nonlinear elliptic problems. I will initially recall some results known for uniformly elliptic problems then turning to non-uniformly elliptic ones.



  • 10 pm Beijing Time (GMT+8):


Speaker: Sun-Sig Byun, Seoul National University, Korea.


Title: Global regularity estimates for nonlinear elliptic equations with nonstandard growth, Part 1

Abstract: A general class of nonlinear elliptic equations with nonstandard growth in nonsmooth domains is considered for the study of global gradient estimates of solutions.



2. May 2nd, 2020


  • 9 pm Beijing Time (GMT+8):


Speaker: Giuseppe Mingione, University of Parma, Italy.


Title: Gradient estimates from uniformly to non-uniformly elliptic problems, Part 2


Abstract: I will give an overview of pointwise gradient estimates for solutions to nonlinear elliptic problems. I will initially recall some results known for uniformly elliptic problems then turning to non-uniformly elliptic ones.


  • 10 pm Beijing Time (GMT+8):


Speaker: Nguyen Cong Phuc, Louisiana State University, USA.


Title: Potential theory and doubly nonlinear PDEs: estimates, existence, and removable sets, Part 1


Abstract: Recent advances in pointwise potential bounds and integral weighted estimates are discussed for a class of quasilinear elliptic equations with measure or distributional data. The connection of those estimates to Sobolev capacities and trace inequalities is presented. Applications include sharp existence criteria and characterizations of removable singular sets for doubly nonlinear equations of the form $-\Delta_p u= u^q +\sigma$, or $-\Delta_p u= |\nabla u|^q +\sigma$. Here $q>0$ could be arbitrarily large, $\Delta_p$ is the $p$-Laplacian ($p>1$), and $\sigma$ is a measure or sometimes a general signed distribution.




3. May 3rd, 2020

  • 9 pm Beijing Time (GMT+8):


Speaker: Sun-Sig Byun, Seoul National University, Korea.

Title: Global regularity estimates for nonlinear elliptic equations with nonstandard growth, Part 2

Abstract: A general class of nonlinear elliptic equations with nonstandard growth in nonsmooth domains is considered for the study of global gradient estimates of solutions.


  • 10 pm Beijing Time (GMT+8):


Speaker: Nguyen Cong Phuc, Louisiana State University, USA.


Title: Potential theory and doubly nonlinear PDEs: estimates, existence, and removable sets, Part 2


Abstract: Recent advances in pointwise potential bounds and integral weighted estimates are discussed for a class of quasilinear elliptic equations with measure or distributional data. The connection of those estimates to Sobolev capacities and trace inequalities is presented. Applications include sharp existence criteria and characterizations of removable singular sets for doubly nonlinear equations of the form $-\Delta_p u= u^q +\sigma$, or $-\Delta_p u= |\nabla u|^q +\sigma$. Here $q>0$ could be arbitrarily large, $\Delta_p$ is the $p$-Laplacian ($p>1$), and $\sigma$ is a measure or sometimes a general signed distribution.




You could find more information from the link: IMS Lecture Series


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