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

Qingjun Zhao; Qingjun Zhao

doi:10.3934/math.20241704

AIMS Mathematics

2024, Volume 9, Issue 12: 35949-35963. doi: 10.3934/math.20241704

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Research article

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

Qingjun Zhao ^,

School of Economics and Management, Chongqing Normal University, Chongqing 401331, China

Received: 19 October 2024 Revised: 11 December 2024 Accepted: 16 December 2024 Published: 25 December 2024
MSC : 35K99, 97M30

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.
Citation: 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[J]. AIMS Mathematics, 2024, 9(12): 35949-35963. doi: 10.3934/math.20241704

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Abstract

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.

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