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Fourier Method for an Over–Determined Elliptic System with Several Complex Variables

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Abstract

Two boundary value problems are investigated for an over–determined elliptic system with several complex variables in polydisc. Necessary and sufficient conditions for the existence of finitely many linearly independent solutions and finitely many solvability conditions are derived. Moreover, the boundary value problem for any number of complex variables is treated in a unified way and the essential difference between the case of one complex variable and that of several complex variables is revealed.

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-Sen (Zhongshan) University, Guangzhou 510275, P. R. China

    Dao Qing Dai

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  1. Dao Qing Dai
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Correspondence to Dao Qing Dai.

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This work is partly supported by NSF of China (10071096,10231040), NSF of GuangDong and ZAAC

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Dai, D.Q. Fourier Method for an Over–Determined Elliptic System with Several Complex Variables. Acta Math Sinica 22, 87–94 (2006). https://doi.org/10.1007/s10114-004-0472-6

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  • DOI: https://doi.org/10.1007/s10114-004-0472-6

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