Complex associated to some systems of PDE

Pierre Bonneau; Emmanuel Mazzilli

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arXiv · 1809.01919

Complex associated to some systems of PDE

Pierre Bonneau·Emmanuel Mazzilli

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Abstract

In [WW1] and [WW2], the author constructed the complex associated to 1-regular functions. This complex is the equivalent of Dolbeault's complex for holomorphic functions if we replace the Cauchy-Riemann equations by the Cauchy-Fueter equations. In this paper, using the Cartan theory of linear Pfaffian system, we give a direct construction for the Cauchy-Fueter complex, at least in $\R^8$. Moreover, we give a sufficient condition in terms of Cartan's theory, to ensure that a complex associated to a linear PDE system with constant coefficients of order one, contains only operators of order one. In fact, the Cauchy-Fueter equation in $\R^8$ is an illuminating example for which this condition is not satisfied

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Pierre Bonneau, Emmanuel Mazzilli. 2018-09-06. Complex associated to some systems of PDE. https://arxiv.org/abs/1809.01919

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