PDE 2 lecture homepage

Oral exams are on July 10th-12th, 2024, 13:00-17:00. The oral exam is 15 mins and based on the lecture.

Preliminary syllabus:

• Sobolev spaces (Sobolev embeddings, trace operator)
• Functional analytic tools
• Elliptic equations (existence, regularity)
• Hyperbolic equations (existence, regularity, decay)

Literature for the lecture:

• "Partial Differential Equations", Evans
• "Elliptic Partial Differential Equations of Second Order", Gilbarg-Trudinger
• "Nonlinear dispersive equations", Terence Tao

Literature for the seminar:

• "General Relativity", Wald
• Lecture notes on General Relativity, S. Aretakis link
• "The Cauchy Problem in General Relativity", H. Ringstrom link
• The characteristic gluing problem for the scalar wave equation, Aretakis link

Seminar talk is 45mins, with accompanying LaTeX write up. Here is the seminar schedule