Local max-norm regularity estimates for gradient solutions of variational inequalities involving a class of doubly degenerate parabolic operators arising from quanto option valuation analysis

Wenwen Jiang; Jia Li; Wenwen Jiang; Jia Li

doi:10.3934/math.2025975

AIMS Mathematics

2025, Volume 10, Issue 9: 21902-21915. doi: 10.3934/math.2025975

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Research article

Local max-norm regularity estimates for gradient solutions of variational inequalities involving a class of doubly degenerate parabolic operators arising from quanto option valuation analysis

Wenwen Jiang ,
Jia Li ^,

School of Management, Shenyang Urban Construction University, Shenyang, Liaoning 110167, China

Received: 03 July 2025 Revised: 09 September 2025 Accepted: 11 September 2025 Published: 22 September 2025
MSC : 35M13, 97M40

This paper investigates a class of variational inequality problems governed by double-phase degenerate parabolic operators on cylindrical domains within bounded open sets, which arises from sensitivity analysis of quanto option valuation. The main result establishes max-norm regularity estimates for gradient solutions of the variational inequality.
- initial-boundary value problem for variational inequality,
- gradient solution,
- boundedness in the sup-norm,
- max-norm regularity estimate
Citation: Wenwen Jiang, Jia Li. Local max-norm regularity estimates for gradient solutions of variational inequalities involving a class of doubly degenerate parabolic operators arising from quanto option valuation analysis[J]. AIMS Mathematics, 2025, 10(9): 21902-21915. doi: 10.3934/math.2025975

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Abstract

This paper investigates a class of variational inequality problems governed by double-phase degenerate parabolic operators on cylindrical domains within bounded open sets, which arises from sensitivity analysis of quanto option valuation. The main result establishes max-norm regularity estimates for gradient solutions of the variational inequality.

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