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Research Article | Open Access

The L∞ estimate of the spatial gradient of the solution to a variational inequality problem originates from the financial contract problem with advanced implementation clauses

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

Keywords

variational inequality problemparabolic Kirchhoff operatorL∞ estimate of the spatial gradient of the solutionenergy inequalityCaffarelli–Kohn–Nirenberge inequalityfinancial contract problem
CLC number: 35K99, 97M30

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 35949-35963
DOI: 10.3934/math.20241704

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Zhao Q. The L∞ 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, 2024, 9(12): 35949-35963. https://doi.org/10.3934/math.20241704

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Received: 19 October 2024
Revised: 11 December 2024
Accepted: 16 December 2024
Published: 15 December 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)