Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators

Stefano Biagi; Ermanno Lanconelli

Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators

Analysis of PDEs 2019-08-28 v1

Authors: Stefano Biagi , Ermanno Lanconelli

Abstract

Maximum Principles on unbounded domains play a crucial r\^ole in several problems related to linear second-order PDEs of elliptic and parabolic type. In this paper we consider a class of sub-elliptic operators $\mathcal{L}$ in $\mathbb{R}^N$ and we establish some criteria for an unbounded open set to be a Maximum Principle set for $\mathcal{L}$ . We extend some classical results related to the Laplacian (by Deny, Hayman and Kennedy) and to the sub-Laplacians on stratified Lie groups (by Bonfiglioli and the second-named author).

Keywords

maximal operators combinatorial group theory elliptic partial differential equations

Cite

@article{arxiv.1908.10257,
  title  = {Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators},
  author = {Stefano Biagi and Ermanno Lanconelli},
  journal= {arXiv preprint arXiv:1908.10257},
  year   = {2019}
}

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