Large sets at infinity and Maximum Principle on unbounded domains for a class of sub-elliptic operators
| Autor: | Ermanno Lanconelli, Stefano Biagi |
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| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Pure mathematics media_common.quotation_subject Open set Type (model theory) 01 natural sciences Mathematics - Analysis of PDEs Maximum principle FOS: Mathematics Subharmonic and superharmonic functions 0101 mathematics media_common Mathematics Applied Mathematics 010102 general mathematics Lie group Primary: 35B50 35J70 Secondary: 31C05 Infinity 010101 applied mathematics Elliptic operator Sub-elliptic operators Homogeneous Hörmander operators Laplace operator Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Differential Equations. 269:9680-9719 |
| ISSN: | 0022-0396 |
| Popis: | 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). |
| Databáze: | OpenAIRE |
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