 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2022

Paper 107

The <Weak Harnack inequality> states that there are $p>0$ and $C=C(n,\lambda,\Lambda)$ such that every nonnegative weak supersolution satisfies
$$
\boxed{
\left(\frac1{|B_{3/4}|}\int_{B_{3/4}}u^p\right)^{1/p}
\leq C\inf_{B_{1/2}}u.}
$$
The radii may be replaced by any fixed nested pair of balls, with the constant adjusted accordingly.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 107 / 4 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 107 / 4 / a / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 107 / 4 / a / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)