Maximum principles for some quasilinear elliptic systems

Bibliographic Details
Main Author: Leonardi, Salvatore
Publication Date: 2020
Other Authors: Leonetti, Francesco, Pignotti, Cristina, Rocha, Eugénio, Staicu, Vasile
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/25838
Summary: We give maximum principles for solutions u:Ω→ℝ N to a class of quasilinear elliptic systems whose prototype is [Formula presented]where α∈{1,…,N} is the equation index and Ω is an open, bounded subset of ℝ n . We assume that coefficients [Formula presented] are measurable with respect to x, continuous with respect to y∈ℝ N , bounded and elliptic. In vectorial problems, when trying to bound the solution by means of the boundary data, we need to bypass De Giorgi's counterexample by means of some additional structure assumptions on the coefficients [Formula presented]. In this paper, we assume that off-diagonal coefficients [Formula presented], α≠β, have support in some staircase set along the diagonal in the y α ,y β plane
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spelling Maximum principles for some quasilinear elliptic systemsElliptic systemMaximum principler-staircase supportWe give maximum principles for solutions u:Ω→ℝ N to a class of quasilinear elliptic systems whose prototype is [Formula presented]where α∈{1,…,N} is the equation index and Ω is an open, bounded subset of ℝ n . We assume that coefficients [Formula presented] are measurable with respect to x, continuous with respect to y∈ℝ N , bounded and elliptic. In vectorial problems, when trying to bound the solution by means of the boundary data, we need to bypass De Giorgi's counterexample by means of some additional structure assumptions on the coefficients [Formula presented]. In this paper, we assume that off-diagonal coefficients [Formula presented], α≠β, have support in some staircase set along the diagonal in the y α ,y β planeElsevier2020-12-01T00:00:00Z2020-05-01T00:00:00Z2020-05info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/25838eng0362-546X10.1016/j.na.2018.11.004Leonardi, SalvatoreLeonetti, FrancescoPignotti, CristinaRocha, EugénioStaicu, Vasileinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T04:19:59Zoai:ria.ua.pt:10773/25838Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:05:02.793503Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Maximum principles for some quasilinear elliptic systems
title Maximum principles for some quasilinear elliptic systems
spellingShingle Maximum principles for some quasilinear elliptic systems
Leonardi, Salvatore
Elliptic system
Maximum principle
r-staircase support
title_short Maximum principles for some quasilinear elliptic systems
title_full Maximum principles for some quasilinear elliptic systems
title_fullStr Maximum principles for some quasilinear elliptic systems
title_full_unstemmed Maximum principles for some quasilinear elliptic systems
title_sort Maximum principles for some quasilinear elliptic systems
author Leonardi, Salvatore
author_facet Leonardi, Salvatore
Leonetti, Francesco
Pignotti, Cristina
Rocha, Eugénio
Staicu, Vasile
author_role author
author2 Leonetti, Francesco
Pignotti, Cristina
Rocha, Eugénio
Staicu, Vasile
author2_role author
author
author
author
dc.contributor.author.fl_str_mv Leonardi, Salvatore
Leonetti, Francesco
Pignotti, Cristina
Rocha, Eugénio
Staicu, Vasile
dc.subject.por.fl_str_mv Elliptic system
Maximum principle
r-staircase support
topic Elliptic system
Maximum principle
r-staircase support
description We give maximum principles for solutions u:Ω→ℝ N to a class of quasilinear elliptic systems whose prototype is [Formula presented]where α∈{1,…,N} is the equation index and Ω is an open, bounded subset of ℝ n . We assume that coefficients [Formula presented] are measurable with respect to x, continuous with respect to y∈ℝ N , bounded and elliptic. In vectorial problems, when trying to bound the solution by means of the boundary data, we need to bypass De Giorgi's counterexample by means of some additional structure assumptions on the coefficients [Formula presented]. In this paper, we assume that off-diagonal coefficients [Formula presented], α≠β, have support in some staircase set along the diagonal in the y α ,y β plane
publishDate 2020
dc.date.none.fl_str_mv 2020-12-01T00:00:00Z
2020-05-01T00:00:00Z
2020-05
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/25838
url http://hdl.handle.net/10773/25838
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0362-546X
10.1016/j.na.2018.11.004
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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