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EnglishWe are concerned with the maximum principle for second-order elliptic operators in unbounded domains. Using a geometric condition, already considered by Berestycki, Nirenberg and Varadhan, and a weak boundary Harnack inequality due to Trudinger, Cabré was able to prove the ABP (Alexandroff–Bakelman–Pucci) estimate for a large class of unbounded domains, obtaining as a consequence the maximum principle for general elliptic operators. In this Note we introduce a weak form of the above geometric condition showing that this is enough to obtain the maximum principle for a larger class of domains.
http://hdl.handle.net/11386/1061249| Titolo: | On the maximum principle for second-order elliptic operators in unbounded domains |
| Autori interni: | VITOLO, Antonio |
| Data di pubblicazione: | 2002 |
| Rivista: | COMPTES RENDUS MATHEMATIQUE |
| Abstract: | We are concerned with the maximum principle for second-order elliptic operators in unbounded domains. Using a geometric condition, already considered by Berestycki, Nirenberg and Varadhan, and a weak boundary Harnack inequality due to Trudinger, Cabré was able to prove the ABP (Alexandroff–Bakelman–Pucci) estimate for a large class of unbounded domains, obtaining as a consequence the maximum principle for general elliptic operators. In this Note we introduce a weak form of the above geometric condition showing that this is enough to obtain the maximum principle for a larger class of domains. |
| Handle: | http://hdl.handle.net/11386/1061249 |
| Appare nelle tipologie: | 1.1.2 Articolo su rivista con ISSN |
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