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2008 On the existence and radial symmetry of maximizers for functionals with critical exponential growth in $\Bbb R^2$
Cristina Tarsi
Differential Integral Equations 21(5-6): 477-495 (2008).

Abstract

We investigate the problem of existence and symmetry of maximizers for \[ S(\alpha,4\pi)=\sup_{\|u\|=1 }{\int_B\left(e^{4\pi u^2}-1\right)|x|^{\alpha}dx,} \] where $B$ is the unit disk in $\mathbb{R}^2$ and $\alpha >0$, proposed by Secchi and Serra in [11]. Through the notion of spherical symmetrization with respect to a measure, we prove that supremum is attained for $\alpha$ small. Furthermore, we prove that $S(\alpha,4\pi)$ is attained by a radial function.

Citation

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Cristina Tarsi. "On the existence and radial symmetry of maximizers for functionals with critical exponential growth in $\Bbb R^2$." Differential Integral Equations 21 (5-6) 477 - 495, 2008.

Information

Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35127
MathSciNet: MR2483265

Subjects:
Primary: 49J10
Secondary: 35J60

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.21 • No. 5-6 • 2008
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