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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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