Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift

2000 ◽  
Author(s):  
Georgii S. Litvinchuk
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Singular Integral ◽  
Boundary Value ◽  
Singular Integral Equations ◽  
Solvability Theory

scholarly journals WELL-POSEDNESS OF POINCARE PROBLEM IN THE CYLINDRICAL DOMAIN FOR A CLASS OF MULTI-DIMENSIONAL ELLIPTIC EQUATIONS

2017 ◽  
Vol 20 (10) ◽  
pp. 17-25
Author(s):  
S.A. Aldashev
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Singular Integral ◽  
Elliptic Equations ◽  
Boundary Value ◽  
Singular Integral Equations ◽  
Cylindrical Domain ◽  
Second Order Elliptic Equations ◽  
Poincaré Problem ◽  
Well Posed

The boundary value problems for second order elliptic equations in domains with edges are well studied. For elliptic equations, boundary-value problems on the plane were shown to be well posed by using methods from the theory of analytic functions of complex variable. When the number of independent variables is greater than two, difficulties of fundamental nature arise. Highly attractive and convenient method of singular integral equations can hardly be applied, because the theory of multidimensional singular integral equations is still incomplete. In this paper with the help of the method suggested by the author, the unique solvability is shown and explicit form of classical solution of Poincare problem in a cylindrical domain for a one class of multidimensional elliptic equations is received.

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