Informal Reading Seminar on PDE and Harmonic Analysis

Announcements

In Winter 2024, we plan to meet Mondays 4 - 6 PM at East Hall 5822, and Fridays 4 - 6 PM at East Hall 3096.
In Fall 2023, we met Fridays 4 - 6 PM at East Hall 1360.

(4/1/2024) Monday 4 - 6 PM, East Hall 1360
(2/22/2024) Thursday 4 - 6 PM, East Hall 4088
(2/16/2024) Friday 4 - 6 PM, East Hall 3096
(12/15/2023) Friday 4 - 6 PM, East Hall 4088
(12/7/2023) Thursday 4 - 6 PM, East Hall 3096

(5/6/2024) Functions with Compactly Supported Fourier Transforms, by Shuhong Yang
(4/5/2024 - 5/3/2024) Layer Potentials on C^{1,\alpha} domains, by Jasper Liang
(4/1/2024) L^p boundedness of Dirichlet-to-Neumann operators, by Jasper Liang
(3/8/2024 - 3/22/2024) Singular solutions to the linear problem yu_x - u_{yy} = 0, by Tian Jing
(2/22/2024) An overview of Dalibard-Marbach-Rax, by Tian Jing
(2/16/2024) Strong solutions and higher regularities of the linear equation yu_x - u_{yy} = f, by Tian Jing
(12/15/2023) Strong solutions to the boundary layer equation, by Tian Jing
(12/7/2023) Weak solutions to the boundary layer equation, by Tian Jing
(12/1/2023) Global well-posedness of one-phase Muskat problem III (zero viscosity limit), by Jasper Liang
(11/10/2023) Estimates in boundary layer equations, by Tian Jing
(11/3/2023) Global well-posedness of one-phase Muskat problem II (global well-posedness of viscosity regularization), by Jasper Liang
(10/27/2023) Harmonic analysis, by Yu Jun Loo
(10/20/2023) Global well-posedness of one-phase Muskat problem I (basic setup), by Jasper Liang
(10/13/2023) Boundary layer equations, by Tian Jing

A nonlinear forward-backward problem, Dalibard, Marbach, and Rax (section 2 for weak solutions of boundary layer equation)
Entropy solutions to a second order forward-backward parabolic differential equation (Lemma 4.11 and Proposition 4.12 for energy estimates of boundary layer equations)
On forward-backward parabolic equations in bounded domains (Theorem 3.1, Theorem 4.1 and Theorem 5.1).

Introduction to Partial Differential Equations, Folland
Elliptic Boundary Value Problems on Lipschitz Domains, Kenig (and references therein). It is from the book Beijing Lectures in Harmonic Analysis.
Refined Rellich boundary inequalities for the derivatives of a harmonic function, Agrawal and Alazard
Potential Techniques for Boundary Value Problems on C^1 domains, Fabes, Jodeit, and Riviere

Fourier Analysis and Nonlinear Partial Differential Equations, Bahouri, Chemin, and Danchin