Application of Singular Integral Equations in the Boundary Value Problems of Electroelasticity

2002 ◽  
Vol 9 (1) ◽  
pp. 1-12
Author(s):  
L. Bitsadze
Keyword(s):  
Boundary Value Problems ◽  
Existence Theorem ◽  
Integral Equations ◽  
Singular Integral ◽  
Boundary Value ◽  
Three Dimensional ◽  
Singular Integral Equations ◽  
Potential Method ◽  
Uniqueness And Existence ◽  
Symbolic Matrix

Abstract The purpose of this paper is to consider the three-dimensional versions of the theory of electroelasticity for a transversally esotropic body. Applying the potential method and the theory of singular integral equations, the normality of singular integral equations corresponding to the boundary value problems of electroelasticity are proved and the symbolic matrix is calculated. The uniqueness and existence theorem for the basic BVPs of electroelasticity are given.

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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