Sharp bounds for higher Steklov-Dirichlet eigenvalues on domains with spherical holes
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| Format: | Preprint |
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2023
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| _version_ | 1866915726809366528 |
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| author | Basak, Sagar Chorwadwala, Anisa Verma, Sheela |
| author_facet | Basak, Sagar Chorwadwala, Anisa Verma, Sheela |
| contents | We consider mixed Steklov-Dirichlet eigenvalue problem on smooth bounded domains in Riemannian manifolds. Under certain symmetry assumptions on multiconnected domains in $\mathbb{R}^{n}$ with a spherical hole, we obtain isoperimetric inequalities for $k$-th Steklov-Dirichlet eigenvalues for $2 \leq k \leq n+1$. We extend Theorem 3.1 of \cite{gavitone2023isoperimetric} from Euclidean domains to domains in space forms, that is, we obtain sharp lower and upper bounds of the first Steklov-Dirichlet eigenvalue on bounded star-shaped domains in the unit $n$-sphere and in the hyperbolic space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_16889 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp bounds for higher Steklov-Dirichlet eigenvalues on domains with spherical holes Basak, Sagar Chorwadwala, Anisa Verma, Sheela Spectral Theory Analysis of PDEs 58J50, 35P15 We consider mixed Steklov-Dirichlet eigenvalue problem on smooth bounded domains in Riemannian manifolds. Under certain symmetry assumptions on multiconnected domains in $\mathbb{R}^{n}$ with a spherical hole, we obtain isoperimetric inequalities for $k$-th Steklov-Dirichlet eigenvalues for $2 \leq k \leq n+1$. We extend Theorem 3.1 of \cite{gavitone2023isoperimetric} from Euclidean domains to domains in space forms, that is, we obtain sharp lower and upper bounds of the first Steklov-Dirichlet eigenvalue on bounded star-shaped domains in the unit $n$-sphere and in the hyperbolic space. |
| title | Sharp bounds for higher Steklov-Dirichlet eigenvalues on domains with spherical holes |
| topic | Spectral Theory Analysis of PDEs 58J50, 35P15 |
| url | https://arxiv.org/abs/2312.16889 |