For 3D-vector fields we obtain a family of integral inequalities that can be regarded as the Poincaré inequality within the framework of field theory. We establish a connection between solutions to the corresponding integral identities and the solution to the Neumann problem.
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Translated from Problemy Matematicheskogo Analiza 127, 2024, pp. 97-105.
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Dubinskii, Y.A., Zubkov, P.V. The Poincaré Inequality for 3D-Vector Fields and the Neumann Problem. J Math Sci 281, 584–594 (2024). https://doi.org/10.1007/s10958-024-07135-8
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DOI: https://doi.org/10.1007/s10958-024-07135-8