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Radiation Conditions and Integral Representations for Clifford Algebra-Valued Null-Solutions of the Helmholtz Operator

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The goal of this paper is to develop a unified approach to radiation conditions for the entire class of null-solutions of the Helmholtz operator which are Clifford algebra-valued. The latter is an algebraic context which permits the simultaneous consideration of scalarvalued and vector-valued functions, as well as differential forms of any mixed degree. In such a setting, we provide a multitude of novel radiation conditions which naturally contain the classical Sommerfeld and Silver–Müller radiation conditions in the case of null-solutions for the scalar Helmholtz operator and the Maxwell system respectively, and which also encompass as a particular case the radiation condition introduced by McIntosh and Mitrea for perturbed Dirac operators.

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Authors and Affiliations

  1. Instituto de Matemáticas Unidad Cuernavaca, Universidad Nacional Autónoma de México, A.P. 273-3 Admon. 3, Cuernavaca, Morelos, 62251, México

    E. Marmolejo-Olea

  2. Department of Mathematics, Temple University, 1805 N. Broad Street, Philadelphia, PA, 19122, USA

    I. Mitrea

  3. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    D. Mitrea

  4. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    M. Mitrea

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  1. E. Marmolejo-Olea
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  2. I. Mitrea
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  3. D. Mitrea
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  4. M. Mitrea
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Correspondence to I. Mitrea.

Additional information

Translated from Problemy Matematicheskogo Analiza 91, 2018, pp. 79-167.

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Marmolejo-Olea, E., Mitrea, I., Mitrea, D. et al. Radiation Conditions and Integral Representations for Clifford Algebra-Valued Null-Solutions of the Helmholtz Operator. J Math Sci 231, 367–472 (2018). https://doi.org/10.1007/s10958-018-3826-9

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  • DOI: https://doi.org/10.1007/s10958-018-3826-9

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