This exam was written by me, but unlike this year’s exam it was an open book exam. All of these questions would have also been fair game for this year’s exam, but on this year’s in-person exam you should expect to be asked to state a few definitions and results from lectures:
On an in-person version of Question 1, you might be asked to define uniform ellipticity or to state some of the results from Chapter 3 which are needed in the later parts.
On an in-person version of Question 2, you might be asked to define the interior and exterior ball properties, or to state Theorem 4.17 on the existence of solutions to the Dirichlet problem.
On an in-person version of Question 3, you might be asked to recall the Gidas–Ni–Nirenberg theorem or to define subharmonic.
On an in-person version of Question 4, you might be asked to state a couple of the results from Chapter 6 which are needed or to define uniformly parabolic.
