Report
Existence of very weak solutions to nonlinear elliptic equation with nonstandard growth and global weighted gradient estimates
| العنوان: | Existence of very weak solutions to nonlinear elliptic equation with nonstandard growth and global weighted gradient estimates |
|---|---|
| المؤلفون: | Byun, Sun-Sig, Lim, Minkyu |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs |
| الوصف: | We study a general class of quasilinear elliptic equations with nonstandard growth to prove the existence of a very weak solution to such a problem. A key ingredient in the proof is a priori global weighted gradient estimate of a very weak solution, where the right hand side of the equation is the divergence of a vector-valued function with low degree of integrability. To obtain this estimate, we adopt a notion of reverse H\"older class of Muckenhoupt weights. Another crucial part of the proof is a generalized weighted div-curl lemma in the setting of Orlicz spaces. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.11479 |
| رقم الانضمام: | edsarx.2311.11479 |
| قاعدة البيانات: | arXiv |
| ResultId |
1 |
|---|---|
| Header |
edsarx arXiv edsarx.2311.11479 1073 3 Report report 1073.15905761719 |
| PLink |
https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&scope=site&db=edsarx&AN=edsarx.2311.11479&custid=s6537998&authtype=sso |
| FullText |
Array
(
[Availability] => 0
)
Array ( [0] => Array ( [Url] => http://arxiv.org/abs/2311.11479 [Name] => EDS - Arxiv [Category] => fullText [Text] => View record in Arxiv [MouseOverText] => View record in Arxiv ) ) |
| Items |
Array
(
[Name] => Title
[Label] => Title
[Group] => Ti
[Data] => Existence of very weak solutions to nonlinear elliptic equation with nonstandard growth and global weighted gradient estimates
)
Array ( [Name] => Author [Label] => Authors [Group] => Au [Data] => <searchLink fieldCode="AR" term="%22Byun%2C+Sun-Sig%22">Byun, Sun-Sig</searchLink><br /><searchLink fieldCode="AR" term="%22Lim%2C+Minkyu%22">Lim, Minkyu</searchLink> ) Array ( [Name] => DatePubCY [Label] => Publication Year [Group] => Date [Data] => 2023 ) Array ( [Name] => Subset [Label] => Collection [Group] => HoldingsInfo [Data] => Mathematics ) Array ( [Name] => Subject [Label] => Subject Terms [Group] => Su [Data] => <searchLink fieldCode="DE" term="%22Mathematics+-+Analysis+of+PDEs%22">Mathematics - Analysis of PDEs</searchLink> ) Array ( [Name] => Abstract [Label] => Description [Group] => Ab [Data] => We study a general class of quasilinear elliptic equations with nonstandard growth to prove the existence of a very weak solution to such a problem. A key ingredient in the proof is a priori global weighted gradient estimate of a very weak solution, where the right hand side of the equation is the divergence of a vector-valued function with low degree of integrability. To obtain this estimate, we adopt a notion of reverse H\"older class of Muckenhoupt weights. Another crucial part of the proof is a generalized weighted div-curl lemma in the setting of Orlicz spaces. ) Array ( [Name] => TypeDocument [Label] => Document Type [Group] => TypDoc [Data] => Working Paper ) Array ( [Name] => URL [Label] => Access URL [Group] => URL [Data] => <link linkTarget="URL" linkTerm="http://arxiv.org/abs/2311.11479" linkWindow="_blank">http://arxiv.org/abs/2311.11479</link> ) Array ( [Name] => AN [Label] => Accession Number [Group] => ID [Data] => edsarx.2311.11479 ) |
| RecordInfo |
Array
(
[BibEntity] => Array
(
[Subjects] => Array
(
[0] => Array
(
[SubjectFull] => Mathematics - Analysis of PDEs
[Type] => general
)
)
[Titles] => Array
(
[0] => Array
(
[TitleFull] => Existence of very weak solutions to nonlinear elliptic equation with nonstandard growth and global weighted gradient estimates
[Type] => main
)
)
)
[BibRelationships] => Array
(
[HasContributorRelationships] => Array
(
[0] => Array
(
[PersonEntity] => Array
(
[Name] => Array
(
[NameFull] => Byun, Sun-Sig
)
)
)
[1] => Array
(
[PersonEntity] => Array
(
[Name] => Array
(
[NameFull] => Lim, Minkyu
)
)
)
)
[IsPartOfRelationships] => Array
(
[0] => Array
(
[BibEntity] => Array
(
[Dates] => Array
(
[0] => Array
(
[D] => 19
[M] => 11
[Type] => published
[Y] => 2023
)
)
)
)
)
)
)
|
| IllustrationInfo |