RIT on Fully Nonlinear Elliptic Equations

Organizers: Ricardo Nochetto, Wujun Zhang
When: Wednesdays @ 5pm-6pm, starting the first week of February
Where: room TBA
Subtitle: PDE theory and numerical analysis

Fully nonlinear second order elliptic PDEs arise naturally from differential geometry, stochastic control theory, optimal transport and other fields in science and engineering. In this RIT, we will discuss the concept of viscosity solutions and regularity theory of these PDEs. Some possible topics include:

  • fully nonlinear elliptic equations and viscosity solutions
  • Alexandroff-Bakelman-Pucci estimates
  • Harnack inequality and Hölder regularity
  • Uniqueness of solutions
  • W2,p estimates
  • C1, α estimates
  • C2, α estimates

In contrast to an extensive PDE literature, the numerical approximation reduces to a few papers. We would like to discuss some criteria for designing convergent numerical methods and some tools developed recently which are useful to obtain rates of convergence. Some possible topics include:

  • criterion for convergence of numerical methods
  • discrete version of the Alexandroff-Bakelman-Pucci estimate
  • finite element method for linear elliptic equations in non-divergence form
  • numerical method for Monge-Ampere equations

Archives: F2011-S2012 F2012-S2013 F2013-S2014 F2014-S2015 F2015-S2016 F2016-S2017 F2017-S2018 F2018-S2019 F2019-S2020 F2020-S2021 F2021-S2022 F2022-S2023 

  • Predictive Science and Deep Learning - A Bright Future or an Odd Couple?

    Speaker: Wolfgang Dahmen (Aachen, University of South Carolina) - https://sc.edu/study/colleges_schools/artsandsciences/mathematics/our_people/directory/dahmen_wolfgang.php

    When: Wed, September 20, 2023 - 3:15pm
    Where: Kirwan Hall 3206
  • The optimal paper Moebius band

    Speaker: Richard Schwartz (Brown University) - https://www.math.brown.edu/reschwar/

    When: Fri, September 29, 2023 - 3:15pm
    Where: Kirwan Hall 3206
  • Riehl (TBA)

    Speaker: Emily Riehl (Johns Hopkins University) - https://math.jhu.edu/~eriehl/

    When: Fri, October 6, 2023 - 3:15pm
    Where: Kirwan Hall 3206
  • Categorification and geometry

    Speaker: Lars Hesselholt (Nagoya University) - https://www.math.nagoya-u.ac.jp/~larsh/

    When: Fri, October 13, 2023 - 3:15pm
    Where: Kirwan Hall 3206
  • Mathematics Around the Heisenberg Group

    Speaker: Roger Howe (Yale University) - https://www.norbertwiener.umd.edu/fft/2023/Speakers/Roger_Howe.html

    When: Thu, October 26, 2023 - 3:45pm
    Where: Kirwan Hall 3206
  • Decoding Time's Mysteries for Better Predictions

    Speaker: James Howard (Johns Hopkins University) - https://www.norbertwiener.umd.edu/fft/2023/Speakers/James_Howard.html

    When: Thu, October 26, 2023 - 6:45pm
    Where: Kirwan Hall 3206
  • A tale of two invariants

    Speaker: Paul Feehan (Rutgers) - https://sites.math.rutgers.edu/~feehan/

    When: Wed, November 15, 2023 - 3:15pm
    Where: Kirwan Hall 3206
  • Using logic to study homeomorphism groups

    Speaker: Thomas Koberda (University of Virginia) - https://sites.google.com/view/koberdat

    When: Wed, November 29, 2023 - 3:15pm
    Where: Kirwan Hall 3206
  • Generative Models for Implicit Distribution Estimation: a Statistical Perspective

    Speaker: Yun Yang (University of Illinois Urbana-Champaign) - https://sites.google.com/site/yunyangstat/

    When: Thu, January 25, 2024 - 3:30pm
    Where: Kirwan Hall 3206
  • Video Imputation and Prediction Methods with Applications in Space Weather

    Speaker: Yang Chen (University of Michigan) - https://yangchenfunstatistics.github.io/yangchen.github.io/

    When: Tue, January 30, 2024 - 4:00pm
    Where: Kirwan Hall 3206
  • Arboreal Galois groups: an introduction

    Speaker: Robert Benedetto (Amherst College) - https://rlbenedetto.people.amherst.edu/

    When: Wed, February 7, 2024 - 3:15pm
    Where: Kirwan Hall 3206
  • Higher theta series

    Speaker: Zhiwei Yun (MIT) - https://math.mit.edu/~zyun/

    When: Wed, February 28, 2024 - 3:15pm
    Where: Kirwan Hall 3206
  • Random lattices and their applications in number theory, geometry and statistical mechanics

    Speaker: Jens Marklof (School of Mathematics, University of Bristol) - https://www.bristol.ac.uk/people/person/Jens-Marklof-6eb63e14-a018-4833-9cf8-b95272b5a09e/

    When: Fri, March 1, 2024 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Svetlana Jitomirskaya (University of California, Berkeley) - https://math.berkeley.edu/people/faculty/svetlana-jitomirskaya

    When: Thu, March 14, 2024 - 3:00pm
    Where: Kirwan Hall 3206
  • Instantaneous everywhere-blowup of parabolic stochastic PDEs

    Speaker: Davar Khoshnevisan (University of Utah) - http://www.math.utah.edu/~davar/

    When: Wed, April 3, 2024 - 3:15pm
    Where: Kirwan Hall 3206