On the existence of maximizers for functionals with critical exponential growth in R²

2006/09/28 by Cristina Tarsi, Tarsi, Cristina
Computer Science · Mathematics · #46E35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.AP #msc:46E35

paper · pdf · doi:10.48550/arxiv.math/0609791

13 pages

arxiv created 2006/09/28 · openalex publication_date 2006/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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