Work

Geometric Foundations and Nonsmooth Extensions for Harnack Inequalities on Carnot Groups

Year: 2026

Type: preprint

Abstract: This paper supplies the geometric and approximation results needed to extend the smooth Harnack inequalities proved in the companion paper \cite{GutierrezMohammedSmooth} to weak solutions of divergence-form subelliptic equations on Carnot groups. We collect horizontal perimeter, Gauss--Green, coarea, and regular-level-set tools, then approximate measurable coefficients and continuous monotone nonlinearities while preserving the structural bounds and pass the Harnack estimates to the weak limit.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.24013095

Authors: Gutierrez, Cristian E., Mohammed, Ahmed

Institutions: Temple University, Ball State University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225418945

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