Past exam of the mathematics course of the University of Cambridge 2024 iii Paper 107 1 a Solution Created 2026-09-24 Updated 2026-09-25
The operator is strictly elliptic when its symmetric principal matrix is positive definite at every point:It is a uniformly elliptic operator when some satisfiesfor every and . Here the least eigenvalue of the continuous matrix is a positive continuous function on the compact set . It therefore has a positive minimum, which supplies and proves uniform ellipticity.