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Generalized integral representations for functions with values in C(V 3,3)

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Abstract

By using the solution to the Helmholtz equation Δu − λu = 0 (λ ≥ 0), the explicit forms of the so-called kernel functions and the higher order kernel functions are given. Then by the generalized Stokes formula, the integral representation formulas related with the Helmholtz operator for functions with values in C(V 3,3) are obtained. As application of the integral representations, the maximum modulus theorem for function u which satisfies H u = 0 is given.

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Authors and Affiliations

  1. Institut f. Mathematik/Physik, Bauhaus-Universität Weimar, Coudraystr. 13, D-99423, Weimar, Germany

    Klaus Gürlebeck

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Zhongxiang Zhang

Authors
  1. Klaus Gürlebeck
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  2. Zhongxiang Zhang
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Correspondence to Zhongxiang Zhang.

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Project supported by Deutscher Akademischer Austausch Dienst (German Academic Exchange Service) and the National Natural Science Foundation of China (No. 10471107).

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Gürlebeck, K., Zhang, Z. Generalized integral representations for functions with values in C(V 3,3). Chin. Ann. Math. Ser. B 32, 123–138 (2011). https://doi.org/10.1007/s11401-010-0619-y

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  • DOI: https://doi.org/10.1007/s11401-010-0619-y

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