Critical points of arbitrary energy for the Trudinger-Moser functional in planar domains

Given a smoothly bounded non-contractible domain Ω⊂R2, we prove the existence of positive critical points of the Trudinger-Moser embedding for arbitrary Dirichlet energies. This is done via degree theory, sharp compactness estimates and a topological argument relying on the Poincaré-Hopf theorem....

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Veröffentlicht in:	Advances in mathematics (New York. 1965) 2024-04, Vol.442, p.109548, Article 109548
Hauptverfasser:	Malchiodi, Andrea, Martinazzi, Luca, Thizy, Pierre-Damien
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis of PDEs Critical inequalities Leray-Schauder degree Mathematics Moser-Trudinger Poincaré-Hopf theorem
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Given a smoothly bounded non-contractible domain Ω⊂R2, we prove the existence of positive critical points of the Trudinger-Moser embedding for arbitrary Dirichlet energies. This is done via degree theory, sharp compactness estimates and a topological argument relying on the Poincaré-Hopf theorem.
ISSN:	0001-8708 1090-2082
DOI:	10.1016/j.aim.2024.109548