Hartogs Phenomena and Antisyzygies for Systems of Differential Equations |
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| Authors: | Alberto Damiano Daniele Struppa Adrian Vajiac Mihaela Vajiac |
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| Institution: | (1) Department of Mathematics and Computer Science, Chapman University, One University Drive, Orange, CA 92866, USA |
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| Abstract: | We introduce the notion of antisyzygies, which studies the inverse problem of finding a system of PDEs, given compatibility
conditions. The system obtained possesses the property of removability of compact singularities. We write explicit computations
in the cases of the Cauchy-Fueter system and Maxwell’s system for electromagnetism, and we conclude with a study of systems
of non-maximal rank.
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| Keywords: | PDE systems Syzygy Resolutions Compatibility conditions Cauchy-Fueter system Maxwell equations |
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