SOME INTEGRAL REPRESENTATION FORMULAS AND SCHWARZ LEMMAS RELATED TO PERTURBED DIRAC OPERATORS

Longfei Gu; Yuanyuan Liu; Rihang Lin

doi:10.11948/20220033

2022 Volume 12 Issue 6

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Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(6): 2475-2487

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Longfei Gu, Yuanyuan Liu, Rihang Lin. SOME INTEGRAL REPRESENTATION FORMULAS AND SCHWARZ LEMMAS RELATED TO PERTURBED DIRAC OPERATORS[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2475-2487. doi: 10.11948/20220033

Citation:

Longfei Gu, Yuanyuan Liu, Rihang Lin. SOME INTEGRAL REPRESENTATION FORMULAS AND SCHWARZ LEMMAS RELATED TO PERTURBED DIRAC OPERATORS[J]. Journal of Applied Analysis & Computation, 2022, 12(6): 2475-2487. doi: 10.11948/20220033

SOME INTEGRAL REPRESENTATION FORMULAS AND SCHWARZ LEMMAS RELATED TO PERTURBED DIRAC OPERATORS

1.
Department of Mathematics, Linyi University, Linyi Shandong, 276005, China
2.
Department of Mathematics, Qufu Normal University, Qufu Shandong, 273165, China

Corresponding authors: Email: liuyuanyuan1117@163.com(Y. Liu); Email: gulongfei@lyu.edu.cn(L. Gu)
Fund Project: The authors were supported by NSF of Shandong Province (Nos. ZR2021MA079, ZR2022MA093), NSF of China (Nos. 12171221, 12071198), China Postdoctoral Science Foundation (No. 2021M691851) and USIP of Linyi University (No. X202110452285)

Abstract

Abstract

In this paper, we first obtain some integral representations for perturbed Dirac operators by using the fundamental solutions of the modified Helmholtz equation and Clifford calculus approach. Second, based on the exhaustion of arbitrary open subsets and integral representations, we investigate generalized Cauchy type integral representation formulas. Moreover, we establish Schwarz lemmas for the null solutions of perturbed Dirac operators in $ \mathbb{R}^{3} $. Finally, as applications, we solve a kind of Dirichlet boundary value problem for perturbed Dirac operators and give the explicit representation of the solution.
- Clifford analysis /
- integral representations /
- Schwarz Lemma /
- Dirichlet problems
MSC: 30G35, 34B15, 11F85, 32A55

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References

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