On ratios of harmonic functions

05/13/2016 - 13:30
05/13/2016 - 14:30
Eugenia Malinnikova, Trondheim/Purdue
Seminar Montreal Analysis Seminar McGill, Burnside Hall, 805 Sherbrooke Str West, Room 920

 We consider pairs of harmonic functions in the unit ball of R^n with the same zero set Z and prove that the ratio is a well-defined real-analytic function that satisfies the maximum principle, the Harnack inequality and a certain gradient estimate. Some examples of such pairs will be discussed. We will show that he constants in these inequalities depend only on the zero set Z, moreover, in dimension two the dependence is only on the length of the zero set. This is a joint work with A. Logunov.

Last edited by on Mon, 05/09/2016 - 15:49