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Research Article | Open Access

Hölder and Schauder estimates for weak solutions of a certain class of non-divergent variation inequality problems in finance

Yudong Sun1, Tao Wu2,3( )
School of Political and Economic Management, Guizhou Minzu University, Guiyang 550025, China
Guizhou Institute of Minority Education, Guizhou Education University, Guiyang 550018, China
Guizhou Institute for Rural Vitalization, Guizhou Education University, Guiyang 550018, China
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Abstract

This article studies a class of variational inequality problems composed of non-divergence type parabolic operators. In comparison with traditional differential equations, this study focuses on overcoming inequality constraints to obtain Hölder and Schauder estimates for weak solutions. The results indicate that the weak solution of the variational inequality possesses the C α continuity and the Schauder estimate on the W 1 , p space, where α ∈ ( 0 , 1 ) and p ≥ 2.

Keywords

variation-inequality problemsnon-divergence type parabolic operatorHölder and Schauder estimate
CLC number: 35K99, 97M30

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AIMS Mathematics
Volume 8 Issue 8,
August 2023
Pages 18995-19003
DOI: 10.3934/math.2023968

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Cite this article:
Sun Y, Wu T. Hölder and Schauder estimates for weak solutions of a certain class of non-divergent variation inequality problems in finance. AIMS Mathematics, 2023, 8(8): 18995-19003. https://doi.org/10.3934/math.2023968

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Received: 22 April 2023
Revised: 23 May 2023
Accepted: 26 May 2023
Published: 15 August 2023
©2023 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)