Given a smoothly bounded non-contractible domain Omega in R^2, 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; Martinazzi, Luca; Thizy, Pierre-Damien. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 442:(2024). [10.1016/j.aim.2024.109548]
Critical points of arbitrary energy for the Trudinger-Moser functional in planar domains
Malchiodi, Andrea;Martinazzi, Luca;Thizy, Pierre-Damien
2024
Abstract
Given a smoothly bounded non-contractible domain Omega in R^2, 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 allegati a questo prodotto
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