Dirichlet problem for semilinear edge-degenerate elliptic equations with singular potential term (Q765946)
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scientific article; zbMATH DE number 6017660
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dirichlet problem for semilinear edge-degenerate elliptic equations with singular potential term |
scientific article; zbMATH DE number 6017660 |
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Dirichlet problem for semilinear edge-degenerate elliptic equations with singular potential term (English)
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22 March 2012
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The authors introduce weighted \(p\)-Sobolev spaces on manifolds with edge singularities. The Sobolev inequality, Poincaré inequality and Hardy inequality for these spaces are proved. Finally some applications of the obtained inequalities are given for the semilinear elliptic problem with Dirichlet boundary conditions and with singular potentials on manifolds with edge singularities.
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Dirichlet boundary value problem
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singular potential
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Poincaré inequality
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edge Hardy inequality
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Sobolev inequality
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manifolds with edge singularities
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