Uniform a priori estimates for positive solutions of the Lane–Emden system in the plane

Uniform a priori estimates for positive solutions of the Lane–Emden system in the plane

We prove that positive solutions of the superlinear Lane–Emden system in a two-dimensional smooth bounded domain are bounded independently of the exponents in the system, provided the exponents are comparable. As a consequence, the energy of the solutions is uniformly bounded, a crucial information...

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Veröffentlicht in:Calculus of variations and partial differential equations 2023-04, Vol.62 (3), Article 76
Hauptverfasser: Kamburov, Nikola, Sirakov, Boyan
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Exponents
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Theoretical
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Zusammenfassung:We prove that positive solutions of the superlinear Lane–Emden system in a two-dimensional smooth bounded domain are bounded independently of the exponents in the system, provided the exponents are comparable. As a consequence, the energy of the solutions is uniformly bounded, a crucial information in their asymptotic study. In addition, the boundedness may fail if the exponents are not comparable.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-022-02414-1