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Schwarz-Type Lemmas Associated to a Helmholtz Equation

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Abstract

As a case of the Laplacian, the Helmholtz operator can be factorized using perturbed Dirac operators. In this article, we prove Schwarz lemmas for solutions of perturbed Dirac operators in vector space \(\mathbb {R}^{3}\) by the integral representation formulas. As an immediate consequence of the Schwarz lemma, one has Liouville’s theorem for monogenic functions in Clifford analysis.

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Acknowledgements

The authors are very grateful to the reviewers for their suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Linyi University, Linyi, 276005, Shandong, People’s Republic of China

    Longfei Gu

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  1. Longfei Gu
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Correspondence to Longfei Gu.

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Communicated by Swanhild Bernstein

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This work was partially supported by NSF of China (Grant Nos. 11401287, 11701251, 11771195) and AMEP of Linyi University.

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Gu, L. Schwarz-Type Lemmas Associated to a Helmholtz Equation. Adv. Appl. Clifford Algebras 30, 14 (2020). https://doi.org/10.1007/s00006-020-1040-6

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  • DOI: https://doi.org/10.1007/s00006-020-1040-6

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