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arXiv · 2104.08115

Schauder estimates up to the boundary on H-type groups: an approach via the double layer potential

Giovanna Citti·Gianmarco Giovannardi·Yannick Sire
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Abstract

We establish the Schauder estimates at the boundary away from the characteristic points for the Dirichlet problem by means of the double layer potential in a Heisenberg-type group $\mathbb{G}$. Despite its singularity we manage to invert the double layer potential restricted to the boundary thanks to a reflection technique for an approximate operator in $\mathbb{G}$. This is the first instance where a reflection-type argument appears to be useful in the sub-Riemannian setting.

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Giovanna Citti, Gianmarco Giovannardi, Yannick Sire. 2023-02-20. Schauder estimates up to the boundary on H-type groups: an approach via the double layer potential. https://arxiv.org/abs/2104.08115

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