Comparison principles for degenerate sub-elliptic equations in non-divergence form

2024/09/23 by Manfredi, Juan J., Mukherjee, Shirsho
#35H20 #35J92 #35J94 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.15144

Abstract

We prove the comparison principle for viscosity sub/super-solutions of degenerate subelliptic equations in non-divergence form that include the sub-elliptic infinity Laplacian and the normalized p-Laplacian. The equations are defined by a collection of vector fields satisfying Hörmander's rank condition and are left invariant with respect to a nilpotent Lie Group.

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