A free boundary problem for systems (The symmetric regime)
<p dir="ltr">In this short note, we study a system of PDEs with free boundaries inside the unit ball. In particular, we prove that solutions to our problem exist and, furthermore, that any solution must be symmetric.The core difficulty arises from the non-variational nature of the sy...
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| مؤلفون آخرون: | |
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2025
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إضافة وسم
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| _version_ | 1864513522574032896 |
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| author | Layan El Hajj (23275180) |
| author2 | Henrik Shahgholian (23275183) |
| author2_role | author |
| author_facet | Layan El Hajj (23275180) Henrik Shahgholian (23275183) |
| author_role | author |
| dc.creator.none.fl_str_mv | Layan El Hajj (23275180) Henrik Shahgholian (23275183) |
| dc.date.none.fl_str_mv | 2025-02-08T06:00:00Z |
| dc.identifier.none.fl_str_mv | 10.3934/cpaa.2025036 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/A_free_boundary_problem_for_systems_The_symmetric_regime_/31443964 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Mathematical sciences Applied mathematics Pure mathematics Free boundary System Singularities Existence Symmetry |
| dc.title.none.fl_str_mv | A free boundary problem for systems (The symmetric regime) |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">In this short note, we study a system of PDEs with free boundaries inside the unit ball. In particular, we prove that solutions to our problem exist and, furthermore, that any solution must be symmetric.The core difficulty arises from the non-variational nature of the system, coupled with a highly singular right-hand side term. These characteristics preclude the application of standard techniques. However, the inherent symmetry of the problem, derived from the geometry, allows us to circumvent these challenges. Although we treat the Laplacian case in more detail, the approach is easily generalized to more general operators, -component case, and -Laplacian operator as stated in the paper.</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Communications on Pure and Applied Analysis<br>License: <a href="https://creativecommons.org/licenses/by/4.0/deed.en" target="_blank">https://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.3934/cpaa.2025036" target="_blank">https://dx.doi.org/10.3934/cpaa.2025036</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_16a2d22a8bd6615bb253b42dbc233500 |
| identifier_str_mv | 10.3934/cpaa.2025036 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/31443964 |
| publishDate | 2025 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | A free boundary problem for systems (The symmetric regime)Layan El Hajj (23275180)Henrik Shahgholian (23275183)Mathematical sciencesApplied mathematicsPure mathematicsFree boundarySystemSingularitiesExistenceSymmetry<p dir="ltr">In this short note, we study a system of PDEs with free boundaries inside the unit ball. In particular, we prove that solutions to our problem exist and, furthermore, that any solution must be symmetric.The core difficulty arises from the non-variational nature of the system, coupled with a highly singular right-hand side term. These characteristics preclude the application of standard techniques. However, the inherent symmetry of the problem, derived from the geometry, allows us to circumvent these challenges. Although we treat the Laplacian case in more detail, the approach is easily generalized to more general operators, -component case, and -Laplacian operator as stated in the paper.</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Communications on Pure and Applied Analysis<br>License: <a href="https://creativecommons.org/licenses/by/4.0/deed.en" target="_blank">https://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.3934/cpaa.2025036" target="_blank">https://dx.doi.org/10.3934/cpaa.2025036</a></p>2025-02-08T06:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.3934/cpaa.2025036https://figshare.com/articles/journal_contribution/A_free_boundary_problem_for_systems_The_symmetric_regime_/31443964CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/314439642025-02-08T06:00:00Z |
| spellingShingle | A free boundary problem for systems (The symmetric regime) Layan El Hajj (23275180) Mathematical sciences Applied mathematics Pure mathematics Free boundary System Singularities Existence Symmetry |
| status_str | publishedVersion |
| title | A free boundary problem for systems (The symmetric regime) |
| title_full | A free boundary problem for systems (The symmetric regime) |
| title_fullStr | A free boundary problem for systems (The symmetric regime) |
| title_full_unstemmed | A free boundary problem for systems (The symmetric regime) |
| title_short | A free boundary problem for systems (The symmetric regime) |
| title_sort | A free boundary problem for systems (The symmetric regime) |
| topic | Mathematical sciences Applied mathematics Pure mathematics Free boundary System Singularities Existence Symmetry |