Isoperimetric estimates of the second boundary value problem for the Poisson equation

1991 ◽  
Vol 50 (5) ◽  
pp. 1126-1130
Author(s):  
A. A. Kosmodem'yanskii
Keyword(s):  
Boundary Value Problem ◽  
Poisson Equation ◽  
Boundary Value ◽  
The Poisson Equation

scholarly journals Eigenvalues, eigenfunctions and Green's functions on a path via Chebyshev polynomials

2009 ◽  
Vol 3 (2) ◽  
pp. 282-302 ◽  
Author(s):  
E. Bendito ◽  
A.M. Encinas ◽  
A. Carmona
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Poisson Equation ◽  
Chebyshev Polynomials ◽  
Ground State ◽  
Green's Functions ◽  
Periodic Boundary ◽  
Green’S Functions ◽  
Boundary Value ◽  
The Poisson Equation

In this work we analyze the boundary value problems on a path associated with Schr?dinger operators with constant ground state. These problems include the cases in which the boundary has two, one or none vertices. In addition, we study the periodic boundary value problem that corresponds to the Poisson equation in a cycle. Moreover, we obtain the Green's function for each regular problem and the eigenvalues and their corresponding eigenfunctions otherwise. In each case, the Green's functions, the eigenvalues and the eigenfunctions are given in terms of first, second and third kind Chebyshev polynomials.

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