Best constant and mountain-pass solutions for a supercritical Hardy-Sobolev problem in the presence of symmetries (Q6112492)
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scientific article; zbMATH DE number 7723303
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Best constant and mountain-pass solutions for a supercritical Hardy-Sobolev problem in the presence of symmetries |
scientific article; zbMATH DE number 7723303 |
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Best constant and mountain-pass solutions for a supercritical Hardy-Sobolev problem in the presence of symmetries (English)
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7 August 2023
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Let \(G\) be a group of isometries of a Riemannian manifold. The author looks for the existence of \(G\)-invariant positive solutions of a suitable nonlinear equation. Concerning the proof, he uses the Aubin minimization and the Mountain-Pass lemma of Ambrosetti-Rabinowitz. Also, he finds the best constant in the associated Hardy-Sobolev inequality.
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elliptic equations
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supercritical exponent
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symmetries
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