A Bounded mean oscillation (BMO) theorem for small distorted diffeomorphisms from $\mathbb R^D$ to $\mathbb R^D$ and PDE

TL;DR

This paper establishes a BMO theorem for small distorted diffeomorphisms in Euclidean space, linking geometric distortions to PDE properties, with implications for understanding the regularity of such mappings.

Contribution

It introduces a bounded mean oscillation theorem specifically for small distorted diffeomorphisms, extending the theoretical framework for analyzing geometric distortions in PDE contexts.

Findings

BMO bounds for small distorted diffeomorphisms

Connection between geometric distortion and PDE regularity

Extension of classical BMO results to nonlinear mappings

Abstract

This announcement considers the following problem. We produce a bounded mean oscillation theorem for small distorted diffeomorphisms from $\mathbb R^D$ to $\mathbb R^D$. A revision of this announcement is in the memoir preprint: arXiv:2103.09748, [1], submitted for consideration for publication.