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

Cristina Tarsi

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

Cristina Tarsi

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Abstract

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.

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Cristina Tarsi. 2006-09-28. On the existence of maximizers for functionals with critical exponential growth in R^2. https://arxiv.org/abs/math/0609791

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