We study the John-Stromberg inequality over families of general sets in topological measure spaces satisfying certain axioms, which include families of sections induced by strictly convex functions in $\Bbb R^n$. Affine VMO space is introduced and studied. Then we will present a regularity theory for entire solutions of locally nondegenerate Monge-Ampere equation $\det D^2u=f(x)$ with $f$ in local affine VMO space.
|Effective start/end date||1/08/21 → 31/07/22|
UN Sustainable Development Goals
In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This project contributes towards the following SDG(s):
- John-Stromberg inequality
- affine VMO
- Monge-Ampere equation
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