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
• Lecture notes (here) by Jonathan Luk

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 and below you find the scripts for each talk.