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

We study the asymptotic behavior of positive solutions of fully nonlinear elliptic equations in a ball, as the exponent of the power nonlinearity approaches a critical value. We show that solutions concentrate and blow up at the center of the ball, while a suitable associated energy remains invarian...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2018-12, Vol.57 (6), p.1-22, Article 158
Main Authors: Birindelli, Isabeau, Galise, Giulio, Leoni, Fabiana, Pacella, Filomena
Format: Article
Language:English
Subjects:
Analysis
Asymptotic properties
Calculus of Variations and Optimal Control
Optimization
Control
Elliptic functions
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonlinear equations
Nonlinearity
Systems Theory
Theoretical
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Summary:We study the asymptotic behavior of positive solutions of fully nonlinear elliptic equations in a ball, as the exponent of the power nonlinearity approaches a critical value. We show that solutions concentrate and blow up at the center of the ball, while a suitable associated energy remains invariant.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-018-1427-6