Difference between revisions of "Functional Analysis II - 2018"
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| + | == Raffael, 06.08.2018, 10:00-10:30== | ||
| + | This is just a draft! If I remember I'll edit this... | ||
| + | |||
| + | 2 defs of h1,0 | ||
| + | Why is h1,0 norm equivalent to h1 norm (statement of poincare) | ||
| + | |||
| + | Decompose h1 into 2 spaces, one of whi h is h1,p | ||
| + | Why is the decomposition a direct sum?? I.e. prove that intersection of h1,0 and the other space (harmonic fcts) is trivial. | ||
| + | Prove this in 2 ways. | ||
| + | 1) using def | ||
| + | 2) using max theory | ||
| + | |||
| + | For which p is cap(0) =0 | ||
| + | |||
| + | What can i say about the solution of lu = f is f is in ck,alpha? | ||
| + | What if f is in hk?? | ||
| + | Then first step of the proof that u is in hk+2 | ||
Revision as of 12:33, 8 August 2018
Please sign with your name and the date on which you had your exam. If you use this wiki, contribute to it as well or terrible things will happen to you: like me kicking you with my fists.
Raffael, 06.08.2018, 10:00-10:30
This is just a draft! If I remember I'll edit this...
2 defs of h1,0 Why is h1,0 norm equivalent to h1 norm (statement of poincare)
Decompose h1 into 2 spaces, one of whi h is h1,p Why is the decomposition a direct sum?? I.e. prove that intersection of h1,0 and the other space (harmonic fcts) is trivial. Prove this in 2 ways. 1) using def 2) using max theory
For which p is cap(0) =0
What can i say about the solution of lu = f is f is in ck,alpha? What if f is in hk?? Then first step of the proof that u is in hk+2
Raffael, 06.08.2018, 10:00-10:30
Topics:
- Weak form of PDE's
- Poisson equation with Dirichlet data and uniqueness of the solution
- Schauder estimates (just statements, no prooves)
- Elliptic regularity, especially the final theorem of that chapter, idea about H1 estimates
- Application of the strong maximum principle
In general he is very polite and patient. Often if one doesn't know the answer at first shot he will give some time to think about it and also helps you with hints. The exam is on the blackboard but often he only asks you to write down little bits and explain the rest orally. It seemed to me that he is well aware of my nervousness and tried to calm me down by the way he phrased his questions. Over all it was definitely one of my most relaxed oral exams I have had at ETH so far.
