arXiv:math/0609791 Abstract

arXiv:math/0609791 [math.AP]Abstract References Reviews Resources

On the existence of maximizers for functionals with critical exponential growth in R^2

Published 2006-09-28Version 1

In this paper we establish the existence of extremal functions for weighted functionals with critical exponential growth in R^2, which arise from Henon-type equations. The proof is based on the notion of spherical symmetrization with respect to a measure, which allows us to reduce the problem to a one dimensional functional as in the proof due to Carleson and Chang for the unweighted case.

Comments: 13 pages

Categories: math.AP

Subjects: 46E35

Keywords: critical exponential growth, maximizers, extremal functions, henon-type equations, dimensional functional

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