Anisotropic estimates of subelliptic type

TL;DR

This paper investigates subelliptic estimates linked to vector fields satisfying Hörmander's condition, utilizing approximate exponential maps to advance understanding in the regularity theory of degenerate elliptic equations.

Contribution

It introduces a novel approach using approximate exponential maps to derive subelliptic estimates for vector fields satisfying Hörmander's condition.

Findings

Derived new subelliptic estimates for vector fields

Connected estimates to regularity of degenerate elliptic equations

Enhanced understanding of weak solution regularity

Abstract

We discuss some estimates of subelliptic type related with vector fields satisfying the H\"ormander condition. Our approach makes use of a class of approximate exponentials maps. Such kind of estimates arises naturally in the study of regularity theory of weak solutions of degenerate elliptic equations.