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arXiv · 2604.12291

Comparison theorems for weak solutions of nonlinear maximally sub-elliptic PDEs

Gautam Neelakantan Memana
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Abstract

We establish a comparison principle for viscosity subsolutions and supersolutions of a broad class of second-order quasilinear, maximally subelliptic PDEs on general manifolds. In fact, we prove the comparison theorem for a larger class of degenerate subelliptic PDEs. Our result strengthens a recent theorem of Manfredi-Mukherjee, which was established in the setting of Carnot groups. Our main aim is to highlight that maximal subellipticity allows one to obtain a comparison principle for weak solutions in close analogy with the classical elliptic theory.

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Gautam Neelakantan Memana. 2026-04-14. Comparison theorems for weak solutions of nonlinear maximally sub-elliptic PDEs. https://arxiv.org/abs/2604.12291

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