Course syllabus
Tentative lecture plan
Lec 1-2. Introduction, convex function, Dirichlet's principle
Lec 3-6, One-dimensional problems
Lec 7-10, Sobolev spaces
Lec 11-15, Direct methods
Lec 16-17, time for repetition and extra problems
List of possible questions/subjects for the oral exam Download List of possible questions/subjects for the oral exam
Lecture notes
Slides from Lecture 1 Download Slides from Lecture 1
Notes from Lecture 1 Download Notes from Lecture 1
Notes from Lecture 2 Download Notes from Lecture 2
Notes for Lecture 3 Download Notes for Lecture 3
Some related references for Lecture 3: For some details on the Brachistochrone and the cycloid Links to an external site., see also page 45 in One-dimensional Variational Problems. Links to an external site. See also here Links to an external site. for two detailed proofs that the solution is a cycloid.
Notes for Lecture 4 Download Notes for Lecture 4
Notes for Lecture 5 Download Notes for Lecture 5
Notes for Lecture 6 Download Notes for Lecture 6
More notes for Lecture 6 Download More notes for Lecture 6
Further references for Sobolev spaces: Most of the needed results can be found in Juha Kinnunen's lecture notes Links to an external site. and/or Chapter 5 in Craig Evans PDE book Links to an external site..
Notes for Lecture 7 Download Notes for Lecture 7
Notes for Lecture 8 Download Notes for Lecture 8
Notes for Lecture 9 Download Notes for Lecture 9
Notes for Lecture 10 Download Notes for Lecture 10
Notes for Lecture 11 Download Notes for Lecture 11
Notes for Lecture 12 Download Notes for Lecture 12
Notes for Lecture 13 Download Notes for Lecture 13
Notes for Lecture 14 Download Notes for Lecture 14
Notes for Lecture 15 Download Notes for Lecture 15
Additional notes for Lecture 15 Download Additional notes for Lecture 15
Notes for Lecture 16 Download Notes for Lecture 16
For further reading on regularity of nonlinear PDEs: