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arXiv · 2609.00245

Higher-order Gaussian bounds for maximally subelliptic boundary value problems

Brian Street
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Abstract

We establish higher-order Gaussian upper bounds for the heat semigroups associated with a broad class of sectorial maximally subelliptic quadratic forms on manifolds with boundary. Near non-characteristic boundary points and in the interior, we obtain pointwise bounds for all mixed derivatives of the heat kernel in time and along the H\"ormander vector fields, expressed in the associated Carnot--Carath\'eodory geometry. The results apply to operators of arbitrary even order, systems, nonsymmetric forms, and boundary conditions beyond the Dirichlet case.

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Brian Street. 2026-08-31. Higher-order Gaussian bounds for maximally subelliptic boundary value problems. https://arxiv.org/abs/2609.00245

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