The eigenvalue problem for the Laplacian equations |
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| Authors: | Zhiqiang Shao Jiaxing Hong |
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| Affiliation: | aDepartment of Mathematics, Fuzhou University, Fuzhou 350002, China;bInstitute of Mathematics, Fudan University, Shanghai 200433, China |
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| Abstract: | This article studies the Dirichlet eigenvalue problem for the Laplacian equations Δu =-λ u, χ Ω, u=0, δΩ, where Ω  Rn is a smooth bounded convex domain. By using the method of appropriate barrier function combined with the maximum principle, authors obtain a sharp lower bound of the difference of the first two eigenvalues for the Dirichlet eigenvalue problem. This study improves the result of S.T. Yau et al. |
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| Keywords: | Dirichlet eigenvalue problem gradient estimate maximum principle barrier function |
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