The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞
<p dir="ltr">The aim of this paper is to investigate the asymptotic behavior of the minimizers to the following problems related to the fractional p-Laplacian with nonhomogeneous term ℎ(,) in the presence of an obstacle ψ in a bounded Lipschitz domain Ω⊂ℝ ,min{12∫Ω×Ω|()−()||−|+...
محفوظ في:
| المؤلف الرئيسي: | |
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| منشور في: |
2025
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| الموضوعات: | |
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| _version_ | 1864513531465957376 |
|---|---|
| author | Samer Dweik (22047329) |
| author_facet | Samer Dweik (22047329) |
| author_role | author |
| dc.creator.none.fl_str_mv | Samer Dweik (22047329) |
| dc.date.none.fl_str_mv | 2025-08-29T09:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1515/forum-2025-0085 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/The_limit_of_a_nonlocal_i_p_i_-Laplacian_obstacle_problem_with_nonhomogeneous_term_as_i_p_i_/30971341 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Engineering Materials engineering Mathematical sciences Applied mathematics Mathematical physics Infinity fractional Laplacian nonhomogeneous term obstacle problem |
| dc.title.none.fl_str_mv | The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞ |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">The aim of this paper is to investigate the asymptotic behavior of the minimizers to the following problems related to the fractional p-Laplacian with nonhomogeneous term ℎ(,) in the presence of an obstacle ψ in a bounded Lipschitz domain Ω⊂ℝ ,min{12∫Ω×Ω|()−()||−|+∫Ωℎ(,):∈,(Ω),≥ on ¯Ω,= on ∂Ω}.</p><p dir="ltr">In the case when ℎ(,)=ℎ(,) and ℎ(,)≥0 , we show the convergence of the solutions to certain limit as →∞ and identify the limit equation. More precisely, we show that the limit problem is closely related to the infinity fractional Laplacian. In the particular case when ∂ℎ>0 , we study the Hölder regularity of any solution to the limit problem and we extend the existence result to the case when h is not smooth. In addition, we will study the limit of this problem when the nonhomogeneous term ℎ(,) is not necessarily positive. To be more precise, we will consider the following two cases: ℎ(,)=ℎ() and ℎ(,)=ℎ()|| with Λ:=Λ()< .</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Forum Mathematicum<br>License: <a href="http://creativecommons.org/licenses/by/4.0" target="_blank">http://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1515/forum-2025-0085" target="_blank">https://dx.doi.org/10.1515/forum-2025-0085</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_67d1312dca8337af9ff0edbb70439d0a |
| identifier_str_mv | 10.1515/forum-2025-0085 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/30971341 |
| publishDate | 2025 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞Samer Dweik (22047329)EngineeringMaterials engineeringMathematical sciencesApplied mathematicsMathematical physicsInfinity fractional Laplaciannonhomogeneous termobstacle problem<p dir="ltr">The aim of this paper is to investigate the asymptotic behavior of the minimizers to the following problems related to the fractional p-Laplacian with nonhomogeneous term ℎ(,) in the presence of an obstacle ψ in a bounded Lipschitz domain Ω⊂ℝ ,min{12∫Ω×Ω|()−()||−|+∫Ωℎ(,):∈,(Ω),≥ on ¯Ω,= on ∂Ω}.</p><p dir="ltr">In the case when ℎ(,)=ℎ(,) and ℎ(,)≥0 , we show the convergence of the solutions to certain limit as →∞ and identify the limit equation. More precisely, we show that the limit problem is closely related to the infinity fractional Laplacian. In the particular case when ∂ℎ>0 , we study the Hölder regularity of any solution to the limit problem and we extend the existence result to the case when h is not smooth. In addition, we will study the limit of this problem when the nonhomogeneous term ℎ(,) is not necessarily positive. To be more precise, we will consider the following two cases: ℎ(,)=ℎ() and ℎ(,)=ℎ()|| with Λ:=Λ()< .</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Forum Mathematicum<br>License: <a href="http://creativecommons.org/licenses/by/4.0" target="_blank">http://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1515/forum-2025-0085" target="_blank">https://dx.doi.org/10.1515/forum-2025-0085</a></p>2025-08-29T09:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1515/forum-2025-0085https://figshare.com/articles/journal_contribution/The_limit_of_a_nonlocal_i_p_i_-Laplacian_obstacle_problem_with_nonhomogeneous_term_as_i_p_i_/30971341CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/309713412025-08-29T09:00:00Z |
| spellingShingle | The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞ Samer Dweik (22047329) Engineering Materials engineering Mathematical sciences Applied mathematics Mathematical physics Infinity fractional Laplacian nonhomogeneous term obstacle problem |
| status_str | publishedVersion |
| title | The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞ |
| title_full | The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞ |
| title_fullStr | The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞ |
| title_full_unstemmed | The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞ |
| title_short | The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞ |
| title_sort | The limit of a nonlocal <i>p</i>-Laplacian obstacle problem with nonhomogeneous term as <i>p</i>→ ∞ |
| topic | Engineering Materials engineering Mathematical sciences Applied mathematics Mathematical physics Infinity fractional Laplacian nonhomogeneous term obstacle problem |