Given a smoothly bounded non-contractible domain , 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.
Critical points of arbitrary energy for the Trudinger-Moser functional in planar domains
Malchiodi, Andrea
;
2024
Abstract
Given a smoothly bounded non-contractible domain , 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.File in questo prodotto:
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