The $ {L^\infty } $ estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clauses
The present study investigates a class of variational inequality problems under the framework of the parabolic Kirchhoff operator from the financial contract problem. This particular issue stems from the financial contract problem. By utilizing the energy inequality of the obtained solutions, the en...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241704 |
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| _version_ | 1832590788081483776 |
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| author | Qingjun Zhao |
| author_facet | Qingjun Zhao |
| author_sort | Qingjun Zhao |
| collection | DOAJ |
| description | The present study investigates a class of variational inequality problems under the framework of the parabolic Kirchhoff operator from the financial contract problem. This particular issue stems from the financial contract problem. By utilizing the energy inequality of the obtained solutions, the energy inequality of the solution gradients, and the Caffarelli–Kohn–Nirenberge inequality, an estimation of the infinite norm of the solution gradients is obtained. |
| format | Article |
| id | doaj-art-fc30fbc5b43648dea0085917a063fafe |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-fc30fbc5b43648dea0085917a063fafe2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912359493596310.3934/math.20241704The $ {L^\infty } $ estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clausesQingjun Zhao0School of Economics and Management, Chongqing Normal University, Chongqing 401331, ChinaThe present study investigates a class of variational inequality problems under the framework of the parabolic Kirchhoff operator from the financial contract problem. This particular issue stems from the financial contract problem. By utilizing the energy inequality of the obtained solutions, the energy inequality of the solution gradients, and the Caffarelli–Kohn–Nirenberge inequality, an estimation of the infinite norm of the solution gradients is obtained.https://www.aimspress.com/article/doi/10.3934/math.20241704variational inequality problemparabolic kirchhoff operator$ {l^\infty } $ estimate of the spatial gradient of the solutionenergy inequalitycaffarelli–kohn–nirenberge inequalityfinancial contract problem |
| spellingShingle | Qingjun Zhao The $ {L^\infty } $ estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clauses AIMS Mathematics variational inequality problem parabolic kirchhoff operator $ {l^\infty } $ estimate of the spatial gradient of the solution energy inequality caffarelli–kohn–nirenberge inequality financial contract problem |
| title | The $ {L^\infty } $ estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clauses |
| title_full | The $ {L^\infty } $ estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clauses |
| title_fullStr | The $ {L^\infty } $ estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clauses |
| title_full_unstemmed | The $ {L^\infty } $ estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clauses |
| title_short | The $ {L^\infty } $ estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clauses |
| title_sort | l infty estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clauses |
| topic | variational inequality problem parabolic kirchhoff operator $ {l^\infty } $ estimate of the spatial gradient of the solution energy inequality caffarelli–kohn–nirenberge inequality financial contract problem |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241704 |
| work_keys_str_mv | AT qingjunzhao thelinftyestimateofthespatialgradientofthesolutiontoavariationalinequalityproblemoriginatesfromthefinancialcontractproblemwithadvancedimplementationclauses AT qingjunzhao linftyestimateofthespatialgradientofthesolutiontoavariationalinequalityproblemoriginatesfromthefinancialcontractproblemwithadvancedimplementationclauses |