In this paper we give asymptotic estimates of the least energy solution Up of the functional J(u) = ∫Ω |∇u|2 constrained on the manifold ∫Ω |u|p+1 = 1 as p goes to infinity. Here Ω is a smooth bounded domain of ℝ 2. Among other results we give a positive answer to a question raised by Chen, Ni, and Zhou (2000) by showing that lim p→∞ ||up||∞ = √e.
Asymptotic estimates for a two dimensional problem with polynomial nonlinearities / Grossi, Massimo; Adimurthi,. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 132:4(2004), pp. 1013-1019.
Asymptotic estimates for a two dimensional problem with polynomial nonlinearities
GROSSI, Massimo;
2004
Abstract
In this paper we give asymptotic estimates of the least energy solution Up of the functional J(u) = ∫Ω |∇u|2 constrained on the manifold ∫Ω |u|p+1 = 1 as p goes to infinity. Here Ω is a smooth bounded domain of ℝ 2. Among other results we give a positive answer to a question raised by Chen, Ni, and Zhou (2000) by showing that lim p→∞ ||up||∞ = √e.File allegati a questo prodotto
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