Sharp quantization for Lane-Emden problems in dimension two
Pierre-Damien Thizy (ICJ)
TL;DR
This paper proves a precise quantization result for positive solutions of Lane-Emden problems in two-dimensional bounded domains, confirming a conjecture by De Marchis, Ianni, and Pacella.
Contribution
It establishes a sharp quantization theorem for Lane-Emden solutions in 2D, advancing understanding of their asymptotic behavior.
Findings
Proves a sharp quantization for positive solutions in 2D
Confirms a conjecture by De Marchis, Ianni, and Pacella
Enhances understanding of Lane-Emden problem solutions
Abstract
In this short note, we prove a sharp quantization for positive solutions of Lane-Emden problems in a bounded planar domain. This result has been conjectured by De Marchis, Ianni and Pacella [6, Remark 1.2].
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Nonlinear Partial Differential Equations · Advanced Differential Equations and Dynamical Systems