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arXiv · 2510.12529

Harnack inequality for Bessel operators

Giorgio Metafune·Luigi Negro·Chiara Spina
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Abstract

We prove uniqueness results and Harnack inequality for Bessel operators \begin{align*} %\label{def L transf alpha} D_t-\Delta_{x} -2a\cdot\nabla_xD_y- D_{yy}- \frac cy D_y % \nonumber \\[1ex]&=y^{\alpha}\sum_{i,j=1}^{N+1}a_{ij}D_{ij}+y^{\alpha-1}\left(v,\nabla\right)-by^{\alpha-2}. \end{align*} in the strip $[0,T]\times \mathbb{R}^{N+1}_+=\{0 \leq t \leq T, x \in \mathbb{R}^N, y>0\}$ under Neumann boundary conditions at $y=0$.

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Giorgio Metafune, Luigi Negro, Chiara Spina. 2025-10-14. Harnack inequality for Bessel operators. https://arxiv.org/abs/2510.12529

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