Maximum principle for higher order operators in general domains
We first prove De Giorgi type level estimates for functions in W1,t(Ω), Ω⊂RN$ \Omega\subset{\mathbb R}^N $, with t>N≥2$ t \gt N\geq 2 $. This augmented integrability enables us to establish a new Harnack type inequality for functions which do not necessarily belong to De Giorgi’s classes as obtai...
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De Gruyter
2021
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oai:doaj.org-article:368a5e7b8ef14ed7b9353e188f3316052021-12-05T14:10:40ZMaximum principle for higher order operators in general domains2191-94962191-950X10.1515/anona-2021-0210https://doaj.org/article/368a5e7b8ef14ed7b9353e188f3316052021-11-01T00:00:00Zhttps://doi.org/10.1515/anona-2021-0210https://doaj.org/toc/2191-9496https://doaj.org/toc/2191-950XWe first prove De Giorgi type level estimates for functions in W1,t(Ω), Ω⊂RN$ \Omega\subset{\mathbb R}^N $, with t>N≥2$ t \gt N\geq 2 $. This augmented integrability enables us to establish a new Harnack type inequality for functions which do not necessarily belong to De Giorgi’s classes as obtained in Di Benedetto–Trudinger [10] for functions in W1,2(Ω). As a consequence, we prove the validity of the strong maximum principle for uniformly elliptic operators of any even order, in fairly general domains in dimension two and three, provided second order derivatives are taken into account.Cassani DanieleTarsia AntonioDe Gruyterarticleharnack’s inequalityhigher order pdespolyharmonic operatorspositivity preserving property35j3035j4835b50AnalysisQA299.6-433ENAdvances in Nonlinear Analysis, Vol 11, Iss 1, Pp 655-671 (2021) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
harnack’s inequality higher order pdes polyharmonic operators positivity preserving property 35j30 35j48 35b50 Analysis QA299.6-433 |
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harnack’s inequality higher order pdes polyharmonic operators positivity preserving property 35j30 35j48 35b50 Analysis QA299.6-433 Cassani Daniele Tarsia Antonio Maximum principle for higher order operators in general domains |
| description |
We first prove De Giorgi type level estimates for functions in W1,t(Ω), Ω⊂RN$ \Omega\subset{\mathbb R}^N $, with t>N≥2$ t \gt N\geq 2 $. This augmented integrability enables us to establish a new Harnack type inequality for functions which do not necessarily belong to De Giorgi’s classes as obtained in Di Benedetto–Trudinger [10] for functions in W1,2(Ω). As a consequence, we prove the validity of the strong maximum principle for uniformly elliptic operators of any even order, in fairly general domains in dimension two and three, provided second order derivatives are taken into account. |
| format |
article |
| author |
Cassani Daniele Tarsia Antonio |
| author_facet |
Cassani Daniele Tarsia Antonio |
| author_sort |
Cassani Daniele |
| title |
Maximum principle for higher order operators in general domains |
| title_short |
Maximum principle for higher order operators in general domains |
| title_full |
Maximum principle for higher order operators in general domains |
| title_fullStr |
Maximum principle for higher order operators in general domains |
| title_full_unstemmed |
Maximum principle for higher order operators in general domains |
| title_sort |
maximum principle for higher order operators in general domains |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/368a5e7b8ef14ed7b9353e188f331605 |
| work_keys_str_mv |
AT cassanidaniele maximumprincipleforhigherorderoperatorsingeneraldomains AT tarsiaantonio maximumprincipleforhigherorderoperatorsingeneraldomains |
| _version_ |
1718371834030718976 |