The problem of Bitsadze-Samarsky for a degenerating equation of the elliptic type (Q2742850)
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scientific article; zbMATH DE number 1650920
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The problem of Bitsadze-Samarsky for a degenerating equation of the elliptic type |
scientific article; zbMATH DE number 1650920 |
Statements
24 September 2001
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elliptic equation
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degenerate type
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nonlocal boundary value problem
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0.9329194
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0.9268082
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0.9252881
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The problem of Bitsadze-Samarsky for a degenerating equation of the elliptic type (English)
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A nonlocal boundary value problem for an elliptic equation of degenerate type NEWLINE\[NEWLINEy^mu_{xx}+u_{yy}+a(x,y)u_x+ b(x,y)u_y+c(x,y)u=0,\quad m>0NEWLINE\]NEWLINE in the domain \(\Omega\subset\mathbb R^2\) restricted by a curve \(\Gamma\) in the upper half plane and by the segment \([-1,1]\) of the \(x\)-axis is considered. Under some conditions on coefficients \(a,b,c\) and on functions involved in boundary conditions uniqueness of the problem's solution is proved. Existence in the case \(a=b=c=0\) is asserted.
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