Concentration and energy invariance for a class of fully nonlinear\n elliptic equations

2018/02/09 by Isabeau Birindelli, Birindelli, Isabeau, Giulio Galise +5
Computer Science · Mathematics · #34B15 #35B50 #35J60 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1802.03218

openalex publication_date 2018/02/09 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behaviour of positive solutions of fully nonlinear\nelliptic equations in a ball, as the exponent of the power nonlinearity\napproaches a critical value. We show that solutions concentrate and blow up at\nthe center of the ball, while a suitable associated energy remains invariant.\n

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