Тип публикации: статья из журнала
Год издания: 2020
Идентификатор DOI: 10.1142/S0219199719500081
Ключевые слова: Sloshing problem; Dirichlet-to-Neumann operator; mixed Steklov eigenvalue problem; Riesz mean, dirichlet-to-neumann operator, mixed steklov eigenvalue problem, riesz mean, sloshing problem
Аннотация: We study bounds on the Riesz means of the mixed Steklov-Neumann and Steklov-Dirichlet eigenvalue problem on a bounded domain Omega in R-n. 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 asПоказать полностьюymptotically 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.
Журнал: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
Выпуск журнала: vol. 22, Is. 2
ISSN журнала: 02191997
Место издания: SINGAPORE
Издатель: WORLD SCIENTIFIC PUBL CO PTE LTD