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

Zongqi Sun; Zongqi Sun

doi:10.3934/math.2023749

AIMS Mathematics

2023, Volume 8, Issue 6: 14633-14643. doi: 10.3934/math.2023749

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Research article

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

Zongqi Sun ^,

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

Received: 25 February 2023 Revised: 31 March 2023 Accepted: 06 April 2023 Published: 20 April 2023
MSC : 35K99, 97M30

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.
- variation-inequality problems,
- non-Newtonian parabolic operator,
- higher integrability,
- regularity
Citation: Zongqi Sun. Regularity and higher integrability of weak solutions to a class of non-Newtonian variation-inequality problems arising from American lookback options[J]. AIMS Mathematics, 2023, 8(6): 14633-14643. doi: 10.3934/math.2023749

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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.

References

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