Work

Boundedness of weak solutions to degenerate Kolmogorov equations of hypoelliptic type in bounded domains

Year: 2025

Type: article

Abstract: We establish the boundedness of weak subsolutions for a class of degenerate Kolmogorov equations of the hypoelliptic type, compatible with a homogeneous Lie group structure, within bounded product domains using the De Giorgi iteration. We employ the renormalization formula to handle boundary values and provide energy estimates. An – type embedding estimate derived from the fundamental solution is utilized to incorporate lower-order divergence terms. This work naturally extends the boundedness theory for uniformly parabolic equations, with matching exponents for the coefficients.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2025.113794

Author: Mingyi Hou

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Vetenskapsrådet

Award: Degenerate parabolic equations and applications to AI