The weak maximum principle for degenerate elliptic equations: unbounded domains and systems
This paper reviews a number of more or less recent results concerning the validity of Alexandrov-Bakelman-Pucci type estimates and the weak Maximum Principle for non smooth functions satisfying in the viscosity sense fully non linear elliptic partial differential inequalities in unbounded domains. T...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-10-01
|
| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/mine.2020036/fulltext.html |
| _version_ | 1828498635236573184 |
|---|---|
| author | Italo Capuzzo Dolcetta |
| author_facet | Italo Capuzzo Dolcetta |
| author_sort | Italo Capuzzo Dolcetta |
| collection | DOAJ |
| description | This paper reviews a number of more or less recent results concerning the validity of Alexandrov-Bakelman-Pucci type estimates and the weak Maximum Principle for non smooth functions satisfying in the viscosity sense fully non linear elliptic partial differential inequalities in unbounded domains. The last section announces a very recent new result about the validity of the weak Maximum Principle for a class of degenerate elliptic cooperative systems. |
| first_indexed | 2024-12-11T13:10:32Z |
| format | Article |
| id | doaj.art-5823ec6cf3e44731984e9e8f75fade62 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-12-11T13:10:32Z |
| publishDate | 2020-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-5823ec6cf3e44731984e9e8f75fade622022-12-22T01:06:12ZengAIMS PressMathematics in Engineering2640-35012020-10-012477278610.3934/mine.2020036The weak maximum principle for degenerate elliptic equations: unbounded domains and systemsItalo Capuzzo Dolcetta0GNAMPA-INDAM, Roma, ItalyThis paper reviews a number of more or less recent results concerning the validity of Alexandrov-Bakelman-Pucci type estimates and the weak Maximum Principle for non smooth functions satisfying in the viscosity sense fully non linear elliptic partial differential inequalities in unbounded domains. The last section announces a very recent new result about the validity of the weak Maximum Principle for a class of degenerate elliptic cooperative systems.https://www.aimspress.com/article/10.3934/mine.2020036/fulltext.htmlfully nonlinear elliptic differential equationsviscosity solutionsalexandrov-bakelman-pucci estimatesmaximum principlecooperative systems |
| spellingShingle | Italo Capuzzo Dolcetta The weak maximum principle for degenerate elliptic equations: unbounded domains and systems Mathematics in Engineering fully nonlinear elliptic differential equations viscosity solutions alexandrov-bakelman-pucci estimates maximum principle cooperative systems |
| title | The weak maximum principle for degenerate elliptic equations: unbounded domains and systems |
| title_full | The weak maximum principle for degenerate elliptic equations: unbounded domains and systems |
| title_fullStr | The weak maximum principle for degenerate elliptic equations: unbounded domains and systems |
| title_full_unstemmed | The weak maximum principle for degenerate elliptic equations: unbounded domains and systems |
| title_short | The weak maximum principle for degenerate elliptic equations: unbounded domains and systems |
| title_sort | weak maximum principle for degenerate elliptic equations unbounded domains and systems |
| topic | fully nonlinear elliptic differential equations viscosity solutions alexandrov-bakelman-pucci estimates maximum principle cooperative systems |
| url | https://www.aimspress.com/article/10.3934/mine.2020036/fulltext.html |
| work_keys_str_mv | AT italocapuzzodolcetta theweakmaximumprinciplefordegenerateellipticequationsunboundeddomainsandsystems AT italocapuzzodolcetta weakmaximumprinciplefordegenerateellipticequationsunboundeddomainsandsystems |