RIGIDITY AND STABILITY RESULTS FOR THE GAUSS MEAN VALUE FORMULA
Event details
| Date | 13.04.2018 |
| Hour | 14:15 |
| Speaker | Professeur Giovanni Cupini, University de Bologne |
| Location | |
| Category | Conferences - Seminars |
The mean integral of harmonic functions on balls equals the value of these
functions at the center. This is the well known Gauss mean value theorem. In 1972
Kuran proved the reverse: if D is a bounded open set containing x, such that the
mean integral of harmonic functions on D equals the value of these functions at x,
then D is a ball centered at x. Two questions may be raised:
(1) similar rigidity results can be proved for weighted mean integrals?
(2) is the Gauss mean value formula stable? That is: if the mean integral of
harmonic functions on D centered at x is almost equal to the value of these
functions at x, then D is almost a ball with center x?
In this talk I will discuss recent results on these issues obtained in collaboration
with E. Lanconelli (1) and with N. Fusco, E. Lanconelli and X. Zhong (2
)
Links
Practical information
- General public
- Free
Organizer
- Prof. Bernard Dacorogna
Contact
- Virginie Ledouble