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arXiv · 1807.08154

Comparison results for eigenvalues of curlcurl operator and Stokes operator

Zhibing Zhang
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Abstract

This paper mainly establishes comparison results for eigenvalues of $\curl\curl$ operator and Stokes operator. For three-dimensional simply connected bounded domains, the $k$-th eigenvalue of $\curl\curl$ operator under tangent boundary condition or normal boundary condition is strictly smaller than the $k$-th eigenvalue of Stokes operator. For any dimension $n\geq2$, the first eigenvalue of Stokes operator is strictly larger than the first eigenvalue of Dirichlet Laplacian. For three-dimensional strictly convex domains, the first eigenvalue of $\curl\curl$ operator under tangent boundary condition or normal boundary condition is strictly larger than the second eigenvalue of Neumann Laplacian.

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Zhibing Zhang. 2018-07-21. Comparison results for eigenvalues of curlcurl operator and Stokes operator. https://doi.org/10.1007/s00033-018-0997-7

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