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On the de Rham Theorem and an Application to the Maxwell–Stokes Type Problem

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Abstract

In this paper, we derive an \(L^{p}\) version of the de Rham theorem. The key is an \(L^{p}\) version of the Nec̆as inequality. Using this result and the variational method, we show the existence of a solution to the Maxwell–Stokes type system.

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ACKNOWLEDGMENTS

We would like to thank the anonymous referee for his or her very kind advice about an early version of this article.

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  1. Tokyo Denki University, Hatoyama-machi, Japan

    J. Aramaki

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  1. J. Aramaki
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Aramaki, J. On the de Rham Theorem and an Application to the Maxwell–Stokes Type Problem. J. Contemp. Mathemat. Anal. 55, 356–364 (2020). https://doi.org/10.3103/S1068362320060047

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