Seminar | January 29 | 3:40-5 p.m. | 740 Evans Hall
Eugenia Malinnikova, Norwegian University of Science and Technology
The Remez inequality for polynomials states that the maximum of the polynomial over an interval is controlled by its maximum over a subset of the interval of positive measure. The coefficient in the inequality depends on the degree of the polynomial and the result holds in higher dimensions.
We give a version of the Remez inequality for solutions of second order linear elliptic PDEs and their gradients. In this context, the degree of a polynomial is replaced by the Almgren frequency of the solution. We discuss other results on quantitative unique continuation for solutions of elliptic PDEs and their gradients and give some applications for the estimates of eigenfunctions for the Laplace-Beltrami operator. The talk is based on a joint work with A. Logunov.