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• W2057841656 abstract "We study the so-called limiting Sobolev cases for embeddings of the spaces [Formula: see text], where Ω ⊂ ℝ n 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." @default.
• W2057841656 created "2016-06-24" @default.
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• W2057841656 date "2013-03-07" @default.
• W2057841656 modified "2023-10-16" @default.
• W2057841656 title "GROUP INVARIANCE AND POHOZAEV IDENTITY IN MOSER-TYPE INEQUALITIES" @default.
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• W2057841656 doi "https://doi.org/10.1142/s021919971250054x" @default.
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