On the existence of maximizers for functionals with critical exponential growth in R2
Abstract
In this paper we establish the existence of extremal functions for weighted functionals with critical exponential growth in R2, 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.
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