Marcelo Mendes Disconzi
Department of Mathematics, Vanderbilt University

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


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:
Instructor's office hours: Thursdays, 4:007:00pm, or by appointment.
Instructor's office phone: (615) 322-7147.

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

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.

Anonymous feedback
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