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

Yudong Sun; Tao Wu; Yudong Sun; Tao Wu

doi:10.3934/math.2023968

AIMS Mathematics

2023, Volume 8, Issue 8: 18995-19003. doi: 10.3934/math.2023968

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Research article

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

Yudong Sun ¹,
Tao Wu ^{2,3
,
,}

1.
School of Political and Economic Management, Guizhou Minzu University, Guiyang 550025, China
2.
Guizhou Institute of Minority Education, Guizhou Education University, Guiyang 550018, China
3.
Guizhou Institute for Rural Vitalization, Guizhou Education University, Guiyang 550018, China

Received: 22 April 2023 Revised: 23 May 2023 Accepted: 26 May 2023 Published: 05 June 2023
MSC : 35K99, 97M30

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^ \alpha $ continuity and the Schauder estimate on the $ W^{1, p} $ space, where $ \alpha \in (0, 1) $ and $ p\geq 2 $.
- variation-inequality problems,
- non-divergence type parabolic operator,
- Hölder and Schauder estimate
Citation: Yudong Sun, Tao Wu. Hölder and Schauder estimates for weak solutions of a certain class of non-divergent variation inequality problems in finance[J]. AIMS Mathematics, 2023, 8(8): 18995-19003. doi: 10.3934/math.2023968

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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^ \alpha $ continuity and the Schauder estimate on the $ W^{1, p} $ space, where $ \alpha \in (0, 1) $ and $ p\geq 2 $.

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