Timeline for The first eigenvalue of the Schrödinger operator is simple.
Current License: CC BY-SA 3.0
5 events
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| May 8, 2014 at 14:57 | vote | accept | supersnail | ||
| May 20, 2013 at 17:27 | history | edited | Matthias Ludewig | CC BY-SA 3.0 |
deleted 2 characters in body; edited body; added 20 characters in body
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| May 20, 2013 at 14:27 | comment | added | Matthias Ludewig | The argument in the last paragraph also works with $C^2$ instead of $C^\infty$, and the solutions are always $C^2$. You should check out some book about PDE (e.g. the mentioned one by Evans or Gilbarg-Trudinger) to get the exact statements about regularity (especially at the border), but in principle, the same argument should work in most related cases. | |
| May 20, 2013 at 13:37 | comment | added | supersnail | You are using the elliptic regularity. What happens if the potenital V is not smooth but just bounded? I think the eigenfunctions will not be smooth anymore. Does the statement remeins true for this case or are there counterexamples? | |
| May 20, 2013 at 12:26 | history | answered | Matthias Ludewig | CC BY-SA 3.0 |