Lec 26 MVT

[Tse Chiang Chen]

Hi Professor and fellow classmates,
in the mean value theorem, it says that the first term in the right-hand expression (7) is 0, but does not state that the Laplacian is 0. Is the Laplacian assumed to be zero in the notes? And I assume that is how I will prove 2a) of HA8 for a non-zero Laplacian.
Thanks in advance!

[Victor Ivrii]

Hi Professor and fellow classmates,
in the mean value theorem, it says that the first term in the right-hand expression (7) is 0, but does not state that the Laplacian is 0. Is the Laplacian assumed to be zero in the notes?

Yes--in this place, I put it now explicitly.

And I assume that is how I will prove 2a) of HA8 for a non-zero Laplacian.
Thanks in advance!

It has some sign, so instead of equalities you get inequalities.