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

2019/08/27 by Stefano Biagi, Biagi, Stefano, Ermanno Lanconelli +1
Computer Science · Mathematics · #35J70 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary: 35B50 #Secondary: 31C05

paper · pdf · doi:10.48550/arxiv.1908.10257

openalex publication_date 2019/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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