Open Access
Translator Disclaimer
2008 Symmetry of extremal functions in Moser-Trudinger inequalities and a Hénon type problem in dimension two
Denis Bonheure, Enrico Serra, Massimo Tarallo
Adv. Differential Equations 13(1-2): 105-138 (2008).

Abstract

In this paper, we analyze the symmetry properties of maximizers of a Hénon type functional in dimension two. Namely, we study the symmetry of the functions that realize the maximum $$ \sup_{u\in {{H^{1}(\Omega)}}\atop ||u||\le 1} {{\int_\Omega}} \left(e^{\gamma u^2} - 1\right)|x|^\alpha {{\,dx}}, $$ where $\Omega$ is the unit ball of $\mathbb R^2$ and $\alpha,\, \gamma>0$. We identify and study the limit functional $$ \sup_{u\in {{H^{1}(\Omega)}}\atop ||u||\le 1} {{\int_{\partial\Omega}}} \left(e^{\gamma u^2} - 1\right)\,ds, $$ which is the main ingredient to describe the behavior of maximizers as $\alpha\to \infty$. We also consider the limit functional as $\alpha\to 0$ and the properties of its maximizers.

Citation

Download Citation

Denis Bonheure. Enrico Serra. Massimo Tarallo. "Symmetry of extremal functions in Moser-Trudinger inequalities and a Hénon type problem in dimension two." Adv. Differential Equations 13 (1-2) 105 - 138, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1173.35044
MathSciNet: MR2482538

Subjects:
Primary: 35A23
Secondary: 35A15, 35J20, 46E35

Rights: Copyright © 2008 Khayyam Publishing, Inc.

JOURNAL ARTICLE
34 PAGES


SHARE
Vol.13 • No. 1-2 • 2008
Back to Top