Data di Pubblicazione:
2010
Citazione:
New solutions for Trudinger–Moser critical equations in R^2 / M. del Pino, M. Musso, B. Ruf. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 258:2(2010), pp. 421-457. [10.1016/j.jfa.2009.06.018]
Abstract:
Let Ω be a bounded, smooth domain in R^2. We consider critical points of the Trudinger–Moser type
functionals
Given k, we find conditions under which there exists a solution which blows up at exactly k points in
Ω as the parameter λ→0. We find that at least one such solution always exists if k = 2 and Ω is not
simply connected. These results
are existence counterparts of a result by Druet in [O. Druet, Multibump analysis in dimension 2: Quantification
of blow-up levels, Duke Math. J. 132 (2) (2006) 217–269] which classifies asymptotic bounded energy
levels of blow-up solutions for a class of nonlinearities of critical exponential growth.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Blowing-up solutions; Singular perturbations; Trudinger-Moser inequality
Elenco autori:
M. del Pino, M. Musso, B. Ruf
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