The analog of the Schauder inequality for closed surfaces in Euclidean spaces

TL;DR

This paper establishes an analog of the Schauder inequality specifically for closed surfaces embedded in Euclidean spaces, extending classical results to a new geometric context.

Contribution

It introduces a novel inequality analogous to Schauder's for closed surfaces in Euclidean spaces, broadening the scope of classical PDE estimates.

Findings

Derived a Schauder-type inequality for closed surfaces

Extended classical PDE estimates to new geometric settings

Provided foundational results for further geometric analysis

Abstract

The analog of the Schauder inequality for closed surfaces in Euclidean spaces is obtained in this article.