A regularity theorem for fully nonlinear maximally subelliptic PDE

Gautam Neelakantan Memana

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arXiv · 2409.04344

A regularity theorem for fully nonlinear maximally subelliptic PDE

Gautam Neelakantan Memana

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Abstract

We prove a sharp interior regularity theorem for fully nonlinear maximally subelliptic PDE in non-isotropic Sobolev spaces adapted to maximally subelliptic operators. This result complements the regularity theorem proven by Street for adapted Zygmund-H\"older spaces. This also recovers the classical regularity theorem for fully nonlinear elliptic differential operators for classical Sobolev spaces. We also obtain a sharp interior regularity theorem for fully nonlinear maximally subelliptic PDE in isotropic Sobolev spaces.

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Gautam Neelakantan Memana. 2024-09-06. A regularity theorem for fully nonlinear maximally subelliptic PDE. https://arxiv.org/abs/2409.04344

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