| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
I studied eigenvalues and eigenfunctions of the Laplacian. Working jointly with Yohei Sakurai (Saitama university), we obtained concentration inequalities of eigenfunctions of the Laplacian and its nodal sets. We also gave an estimate of eigenvalues of the Laplacian from above in terms of subsets. The domain monotonicity of the eigenvalues of the Laplacian under Neumann boundary conditions on bounded convex domains of Euclidean spaces is studied and sharp inequalities are obtained. Furthermore, universal inequalities are obtained for the eigenvalues of the Laplacian under Neumman boundary conditions on bounded convex domains of Euclidean spaces.
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