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- DANIELE CASSANI
- Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, Como 22100, Italy
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- BERNHARD RUF
- Dipartimento di Matematica "F. Enriques", Università degli Studi di Milano, via C. Saldini 50, Milano 20133, Italy
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- CRISTINA TARSI
- Dipartimento di Matematica "F. Enriques", Università degli Studi di Milano, via C. Saldini 50, Milano 20133, Italy
説明
<jats:p> We study the so-called limiting Sobolev cases for embeddings of the spaces [Formula: see text], where Ω ⊂ ℝ<jats:sup>n</jats:sup> is a bounded domain. Differently from J. Moser, we consider optimal embeddings into Zygmund spaces: we derive related Euler–Lagrange equations, and show that Moser's concentrating sequences are the solutions of these equations and thus realize the best constants of the corresponding embedding inequalities. Furthermore, we exhibit a group invariance, and show that Moser's sequence is generated by this group invariance and that the solutions of the limiting equation are unique up to this invariance. Finally, we derive a Pohozaev-type identity, and use it to prove that equations related to perturbed optimal embeddings do not have solutions. </jats:p>
収録刊行物
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- Communications in Contemporary Mathematics
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Communications in Contemporary Mathematics 15 (02), 1250054-, 2013-03-07
World Scientific Pub Co Pte Lt
