Comparison theorems for weak solutions of nonlinear maximally sub-elliptic PDEs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908962064957440 |
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| author | Memana, Gautam Neelakantan |
| author_facet | Memana, Gautam Neelakantan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_12291 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Comparison theorems for weak solutions of nonlinear maximally sub-elliptic PDEs Memana, Gautam Neelakantan Analysis of PDEs 35H20, 35J94, 35J92 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. |
| title | Comparison theorems for weak solutions of nonlinear maximally sub-elliptic PDEs |
| topic | Analysis of PDEs 35H20, 35J94, 35J92 |
| url | https://arxiv.org/abs/2604.12291 |