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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity
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by Adimurthi and Massimo Grossi PDF
Proc. Amer. Math. Soc. 132 (2004), 1013-1019 Request permission

Abstract:

In this paper we give asymptotic estimates of the least energy solution $u_p$ of the functional \begin{equation*} J(u) =\int _\Omega |\nabla u|^2 \quad \text {constrained on the manifold }\int _\Omega |u|^{p+1}=1\end{equation*} as $p$ goes to infinity. Here $\Omega$ is a smooth bounded domain of $\mathbb {R}^2$. Among other results we give a positive answer to a question raised by Chen, Ni, and Zhou (2000) by showing that $\lim \limits _{p\rightarrow \infty }||u_{p}||_{\infty }=\sqrt e$.
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Additional Information
  • Adimurthi
  • Affiliation: T.I.F.R. Centre, P.O. Box 1234, Bangalore 560012, India
  • Email: aditi@math.tifrbng.res.in
  • Massimo Grossi
  • Affiliation: Università di Roma “La Sapienza", P.le Aldo Moro, 2, 00185 Roma, Italy
  • Email: grossi@mat.uniroma1.it
  • Received by editor(s): September 7, 2002
  • Published electronically: November 10, 2003
  • Additional Notes: Supported by M.U.R.S.T., project “Variational methods and nonlinear differential equations"
  • Communicated by: David S. Tartakoff
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1013-1019
  • MSC (2000): Primary 35J20, 35B40
  • DOI: https://doi.org/10.1090/S0002-9939-03-07301-5
  • MathSciNet review: 2045416