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.

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]

New solutions for Trudinger–Moser critical equations in R^2

B. Ruf
Ultimo
2010

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.
Blowing-up solutions; Singular perturbations; Trudinger-Moser inequality
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/176939
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