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@article{Hassannezhad:2020:10.1142/S0219199719500081,
author = {Hassannezhad, A and Laptev, A},
doi = {10.1142/S0219199719500081},
journal = {Communications in Contemporary Mathematics},
pages = {1--23},
title = {Eigenvalue bounds of mixed Steklov problems},
url = {http://dx.doi.org/10.1142/S0219199719500081},
volume = {22},
year = {2020}
}

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TY  - JOUR
AB  - . The Steklov–Neumann eigenvalue problem is also called the sloshing problem. We obtain two-term asymptotically sharp lower bounds on the Riesz means of the sloshing problem and also provide an asymptotically sharp upper bound for the Riesz means of mixed Steklov–Dirichlet problem. The proof of our results for the sloshing problem uses the average variational principle and monotonicity of sloshing eigenvalues. In the case of Steklov–Dirichlet eigenvalue problem, the proof is based on a well-known bound on the Riesz means of the Dirichlet fractional Laplacian, and an inequality between the Dirichlet and Navier fractional Laplacian. The two-term asymptotic results for the Riesz means of mixed Steklov eigenvalue problems are discussed in the Appendix which in particular show the asymptotic sharpness of the bounds we obtain.
AU  - Hassannezhad,A
AU  - Laptev,A
DO  - 10.1142/S0219199719500081
EP  - 23
PY  - 2020///
SN  - 0219-1997
SP  - 1
TI  - Eigenvalue bounds of mixed Steklov problems
T2  - Communications in Contemporary Mathematics
UR  - http://dx.doi.org/10.1142/S0219199719500081
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000521132600008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://www.worldscientific.com/doi/abs/10.1142/S0219199719500081
UR  - http://hdl.handle.net/10044/1/77937
VL  - 22
ER  -

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