The Neumann problem for semilinear elliptic equations with critical Sobolev exponent (Q931048)
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scientific article; zbMATH DE number 5292360
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Neumann problem for semilinear elliptic equations with critical Sobolev exponent |
scientific article; zbMATH DE number 5292360 |
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The Neumann problem for semilinear elliptic equations with critical Sobolev exponent (English)
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24 June 2008
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This paper is mainly devoted to the study of least energy solutions of a nonlinear elliptic equation with critical Sobolev exponent and Neumann boundary condition. The existence of solutions is deduced with topological linking arguments combined with sharp Sobolev inequalities. This result is then extended to singular potentials by means of the Hardy-Sobolev inequality. Related regularity properties of solutions are also established in the present paper.
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Critical Sobolev exponent
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Hardy-Sobolev potential
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Concentration-compactness principle
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Least energy solutions
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Weighted Sobolev inequalities
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