English

Harnack inequality for Bessel operators

Analysis of PDEs 2025-10-15 v1

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]×R+N+1={0tT,xRN,y>0}[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=0y=0.

Keywords

Cite

@article{arxiv.2510.12529,
  title  = {Harnack inequality for Bessel operators},
  author = {Giorgio Metafune and Luigi Negro and Chiara Spina},
  journal= {arXiv preprint arXiv:2510.12529},
  year   = {2025}
}
R2 v1 2026-07-01T06:36:35.559Z