Removable singularities and Harnack inequality for nonlinear Hörmander degenerate subelliptic equations

2025/10/01 by Yawei Wei, Qiang, Jiayi, Wei, Yawei +2
Mathematics · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2510.00755

openalex publication_date 2025/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper concerns the quasilinear subelliptic function derived from Hörmander vector fields. Based on the significant work of J. Serrin in \citeSER, M. Meier in \citeMM1, and L. Capogna, D. Danielli and N. Garofalo in \citeLC1,LDN, we obtain the removable singularities and Harnack inequality by a sharp Sobolev inequalities under weaker integrability of coefficients in structure conditions. Furthermore, we get the Hölder continuity when domain Ω is equiregular.

Citations

• Sharp embedding results and geometric inequalities for Hörmander vector fields
• Global estimates for the fundamental solution of homogeneous H "ormander\n operators
• Harnack Inequality for a Subelliptic PDE in nondivergence form

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