Some remarks on the Dirichlet problem for an elliptic equation (Q1069034)
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scientific article; zbMATH DE number 3931551
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some remarks on the Dirichlet problem for an elliptic equation |
scientific article; zbMATH DE number 3931551 |
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Some remarks on the Dirichlet problem for an elliptic equation (English)
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1984
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An optimal constant for the inequality \(\| u\|_{p^*,q}\leq K \| \Delta u\|_{L^ p({\mathbb{R}}^ n)},\) \(p^*=np/n-p\), on Lorentz spaces is given. The result is applied to linear and nonlinear elliptic Dirichlet problems.
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Sobolev inequality
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existence
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uniqueness
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optimal constant
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Lorentz spaces
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Dirichlet problems
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