Spectral asymptotics of Laplace operators on surfaces with cusps

1995 ◽  
Vol 303 (1) ◽  
pp. 281-296 ◽  
Author(s):  
L. B. Parnovski
Keyword(s):  
Spectral Asymptotics ◽  
Laplace Operators

ON THE SOLVABILITY OF A MIXED PROBLEM WITH DEGREE LAPLACE OPERATORS WITH NONLOCAL BOUNDARY CONDITIONS

2020 ◽  
pp. 85-104
Author(s):  
Shakirbai G. Kasimov ◽  
◽  
Mahkambek M. Babaev ◽  
◽  
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlocal Boundary Conditions ◽  
Laplace Operators ◽  
Initial Boundary Problem ◽  
Initial Boundary Value ◽  
Delayed Time

The paper studies a problem with initial functions and boundary conditions for partial differential partial equations of fractional order in partial derivatives with a delayed time argument, with degree Laplace operators with spatial variables and nonlocal boundary conditions in Sobolev classes. The solution of the initial boundary-value problem is constructed as the series’ sum in the eigenfunction system of the multidimensional spectral problem. The eigenvalues are found for the spectral problem and the corresponding system of eigenfunctions is constructed. It is shown that the system of eigenfunctions is complete and forms a Riesz basis in the Sobolev subspace. Based on the completeness of the eigenfunctions system the uniqueness theorem for solving the problem is proved. In the Sobolev subspaces the existence of a regular solution to the stated initial-boundary problem is proved.

On eigenvalue problem of the Laplace operators for ellipsoidal areas

2018 ◽  
Vol 2018 (1) ◽  
pp. 146-154
Author(s):  
D.G. Rakhimov ◽  
◽  
Sh.M. Suyarov ◽  
Keyword(s):  
Eigenvalue Problem ◽  
Laplace Operators

scholarly journals Spectral Asymptotics for Stable Trees

2010 ◽  
Vol 15 (0) ◽  
pp. 1772-1801 ◽  
Author(s):  
David Croydon ◽  
Benjamin Hambly
Keyword(s):  
Spectral Asymptotics

scholarly journals Spectral asymptotics of semiclassical unitary operators

2019 ◽  
Vol 473 (2) ◽  
pp. 1174-1202 ◽  
Author(s):  
Yohann Le Floch ◽  
Álvaro Pelayo
Keyword(s):  
Spectral Asymptotics ◽  
Unitary Operators
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