Marcelo Mendes Disconzi
Department of Mathematics, Vanderbilt University

email: marcelo.disconzi at vanderbilt.edu
office: Stevenson Center 1515
phone: (615) 322 7147   fax: (615) 343 0215
mail to: 1326 Stevenson Center, Vanderbilt University, Nashville TN 37240

Vanderbilt












Marcelo Mendes Disconzi
MATH 8110 - Theory of Partial Differential Equations

General Information
For a description of the course, including the grading policy, consult the course syllabus.

Textbook: No textbook will be adopted. Support references are given in the syllabus.

Classes meet on TR, 2:353:50pm, at Stevenson Center 1313 (3rd floor of the Mathematics Building).

Contact Information and Office Hours
Instructor's office: Stevenson Center 1515 (5th floor of the Mathematics Building).
Instructor's email: marcelo.disconzi@vanderbilt.edu.
Instructor's office hours: Thursdays, 4:007:00pm, or by appointment.
Instructor's office phone: (615) 322-7147.

Schedule
Below is an ongoing schedule for the course (for the academic calendar, click here). This will be updated regularly and, therefore, students should check this webpage frequently. The due date for each assignment will be posted as the course progresses.

Date Material covered Remarks
Aug 24
Introduction

Aug 29 Notation and generalities. Harmonic and sub- super- harmonic functions. Mean value formulas, maximum principle, and Harnack's inequality.
Sept 5 Fundamental solution and Green's function, representation formulas, Poisson integral. C^0 sub-harmonic functions and its properties.
Sept 7 Solution to the Dirichlet problem for Laplace's equation via the method of sub-harmonic functions.
Sept 12 The wave equation. D'Alembert's formula, Kirchhoff's formula, and finite speed of propagation.
Sept 19 More on the wave equation. The heat equation.
Sept 21 Weak derivatives. Sobolev spaces.
Sept 26 Basic properties of Sobolev spaces.
Oct 3 More properties of Sobolev spaces. Density and trace theorems.
Oct 5 More properties of Sobolev spaces. Extensions. Holder spaces.
Oct 10 Sobolev inequalities.
Oct 17 More on Sobolev inequalities and compact embeddings.
Oct 27 Linear elliptic equations. Weak solutions. Lax-Milgram.
Oct 31 The Fredholm alternative in Banach spaces.
Nov 2 The Fredholm alternative in Hilbert spaces.
Nov 7 Existence and uniqueness of weak solutions to linear elliptic equations. The weak maximum principle.
Nov 9 Elliptic regularity.
Nov 14 Elliptic regularity up to the boundary.
Nov 16 Basic calculus in Frechet and topological vector spaces.
Nov 28 Inverse and implicit function theorems.
Nov 30 Picard iteration and Newton's method in Banach spaces.
Dec 5 The Nash implicit function theorem.
Dec 7 The Nash isometric embedding theorem.

Anonymous feedback
Students are encouraged to bring suggestions and to discuss with the course instructor any concerns they may have, including something they think is not being properly handled in the course. But if you do not feel comfortable doing that, here you have the opportunity to send some anonymous feedback.