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: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018

  • Augmented reality in the estimation of small tail probabilitiesmall

    Speaker: Benjamin Kedem (UMD) - https://www.math.umd.edu/~bnk/

    When: Wed, September 5, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Aziz Lecture: Smooth random functions and smooth random ODEs

    Speaker: Lloyd N. Trefethan (Oxford University)

    When: Wed, September 12, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Dirac operators and Hecke algebras

    Speaker: Dan Ciubotaru (University of Oxford) - https://www.maths.ox.ac.uk/people/dan.ciubotaru

    When: Wed, September 19, 2018 - 3:15pm
    Where: Chemical Engineering Room 2110
  • Scholze's Fields medal

    Speaker: Michael Rapoport (UMD and University of Bonn) - http://www.math.uni-bonn.de/ag/alggeom/rapoport

    When: Wed, September 26, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • TBA

    Speaker: Marsha Berger (NYU) - https://cs.nyu.edu/berger/

    When: Wed, October 3, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • Topics in Markov chains

    Speaker: Alan Frieze (CMU) - https://www.math.cmu.edu/~af1p/

    When: Fri, October 5, 2018 - 11:00am
    Where: CSIC 4172
  • TBA

    Speaker: Bassam Fayad (Universite de Paris) - https://webusers.imj-prg.fr/~bassam.fayad/

    When: Fri, October 12, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • On traffic modeling and the Braess paradox

    Speaker: Helge Holden (NTNU (Norwegian University of Science and Technology)) - https://www.ntnu.edu/employees/holden

    When: Fri, October 26, 2018 - 3:15pm
    Where: Kirwan Hall 3206
  • -Meeting with the Dean Amitabh Varshney

    Speaker: Department meeting () -

    When: Wed, November 14, 2018 - 3:15pm
    Where: Kirwan Hall 3206