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Research Article | Open Access

Regularity and higher integrability of weak solutions to a class of non-Newtonian variation-inequality problems arising from American lookback options

School of Computer Science, Xijing University, Xi'an, Shaanxi 710123, China
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Abstract

This paper presents the proofs of the higher integrability and regularity of weak solutions to a class of variation-inequality problems that are formulated by a non-Newtonian parabolic operator. After obtaining the gradient estimate, the higher order integrability of the weak solution is analyzed. We also examine the internal regularity estimate of the weak solution by utilizing a test function of the difference type.

Keywords

variation-inequality problemsnon-Newtonian parabolic operatorhigher integrabilityregularity
CLC number: 35K99, 97M30

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AIMS Mathematics
Volume 8 Issue 6,
June 2023
Pages 14633-14643
DOI: 10.3934/math.2023749

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Cite this article:
Sun Z. Regularity and higher integrability of weak solutions to a class of non-Newtonian variation-inequality problems arising from American lookback options. AIMS Mathematics, 2023, 8(6): 14633-14643. https://doi.org/10.3934/math.2023749

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Received: 25 February 2023
Revised: 31 March 2023
Accepted: 06 April 2023
Published: 15 June 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)