On traces of solutions of linear elliptic systems and their application to the Dirichlet problem (Q1090842)
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scientific article; zbMATH DE number 4008925
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On traces of solutions of linear elliptic systems and their application to the Dirichlet problem |
scientific article; zbMATH DE number 4008925 |
Statements
On traces of solutions of linear elliptic systems and their application to the Dirichlet problem (English)
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1986
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We establish a sufficient and necessary condition for a solution of an elliptic system in a smooth domain to have a trace on the boundary in \(L^ 2\). This result is used to derive an energy estimate of a solution in a suitable weighted Sobolev space. As an immediate consequence we obtain the existence of a solution of the Dirichlet problem with \(L^ 2\)-boundary data.
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smooth domain
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trace on the boundary
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energy estimate
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weighted Sobolev space
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existence
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Dirichlet problem
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\(L^ 2\)-boundary data
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