Marcelo Mendes Disconzi
Department of Mathematics, Vanderbilt University

email: marcelo.disconzi at vanderbilt.edu
office: A1017, 17th & Horton (Sony bld)
phone: (615) 322 7147
mail to: 1326 Stevenson Center Ln, 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. Students are responsible for reading the syllabus and being aware of all the course and university policies.

There is no textbook for this course, and we will follow the class notes posted below. Some additional references are suggested in the course syllabus.

Classes meet on TR, 2:45-4pm at Stevenson Center 1312.

Contact Information and Office Hours
Instructor's office: A1017, 17th & Horton (Sony bld).
Instructor's email: marcelo.disconzi@vanderbilt.edu.
Instructor's office hours: Tuesdays, 4:10-6:10pm, Thursdays, 12-1pm, or by appointment.
Instructor's office phone: (615) 322-7147.

Class notes
Click here for the class notes. If you find some inconsistency or something that seems wrong in the class notes, it is likely a typo. In that case, please let the instructor know.

Schedule
Below is schedule for the course which will be updated as the course progresses (for the academic calendar, click here). Sections refer to the class notes. Materials (including HW) will be posted below or on Brightspace.

 Date  Material covered  Remarks
 Aug 21  Introduction. Examples. Sections 1-4.  Homework 1.
 Aug 26  Laplace's and Poisson's equations. Fundamental solution. Existence of solutions to Poisson's equations. Properties of harmonic functions (regularity, mean value, maximum principle, etc.) Section 5.  Homework 2.
 Aug 28  Comments on the heat equation. The wave equation in 1, 2, 3, and arbitrary dimensions: existence and uniqueness, finite propagation speed, Duhamel's formula. Sections 7-8.  Homework 3, Homework 4.
 Sept 2  Weak derivatives, basic properties. Section 9.1.  Homework 5.
 Sept 4  Sobolev spaces. Basic properties. Approximation by smooth functions. Sections 9.2-9.3.  
 Sept 9  No class. Make-up class to be scheduled.  
 Sept 11  No class. Make-up class to be scheduled.  
 Sept 16  The segment condition. Approximation by smooth functions up to the boundary. Change of coordinates. Section 9.3.  
 Sept 18  The strong local Lipschitz, uniform C^k, the cone, and the uniform cone conditions. Extensions. Section 9.4.  Homework 6.
 Sept 23  The Sobolev embedding theorem. Section 9.5.  
 Sept 25  Sobolev inequality. Compact embeddings. Sections 9.6-9.7.  
 Sept 30  Duality. Sobolev spaces of negative order. Comments on traces, Sobolev spaces defined via Fourier transform, and miscellaneous inequalities. Sections 9.8-9.11.  Homework 7.
 Oct 2  Necessary and sufficient conditions for existence of solutions to linear PDEs. Egorov's example of a PDE with no solution. Sections 10-10.1.  
 Oct 7    
 Oct 9  Fall break, no class.  
 Oct 14    
 Oct 16    
 Oct 21    
 Oct 23    
 Oct 28    
 Oct 30    
 Nov 4    
 Nov 6    
 Nov 11    
 Nov 13    
 Nov 18    
 Nov 20    
 Nov 25  Thanksgiving holidays, no class.  
 Nov 27  Thanksgiving holidays, no class.  
 Dec 2    
 Dec 4    


Anonymous feedback
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