dc.creatordel Pino, Manuel
dc.creatorMusso, Monica
dc.creatorRuf, Bernhard
dc.date.accessioned2024-01-10T13:15:31Z
dc.date.accessioned2024-05-02T17:58:27Z
dc.date.available2024-01-10T13:15:31Z
dc.date.available2024-05-02T17:58:27Z
dc.date.created2024-01-10T13:15:31Z
dc.date.issued2010
dc.identifier10.1016/j.jfa.2009.06.018
dc.identifier1096-0783
dc.identifier0022-1236
dc.identifierhttps://doi.org/10.1016/j.jfa.2009.06.018
dc.identifierhttps://repositorio.uc.cl/handle/11534/78507
dc.identifierWOS:000272113100004
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/9269490
dc.description.abstractLet Omega be a bounded, smooth domain in R-2. We consider critical points of the Trudinger-Moser type functional J(lambda) (u) = 1/2 integral(Omega)vertical bar del u vertical bar(2) - lambda/2 integral(Omega)e(u2) in H-0(1)(Omega), namely solutions of the boundary value problem Delta u + lambda ue(u2) = 0 with homogeneous Dirichlet boundary conditions, where lambda > 0 is a small parameter. Given k >= 1 we find conditions under which there exists a solution u(lambda) which blows up at exactly k points in Omega as lambda -> 0 and J(lambda)(u(lambda)) -> 2k pi. We find that at least one such solution always exists if k = 2 and Omega is not simply connected. If Omega has d >= 1 holes, in addition d + 1 bubbling solutions with k = 1 exist. These results are existence counterparts of one 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, including this one as a prototype case. (C) 2009 Elsevier Inc. All rights reserved.
dc.languageen
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE
dc.rightsacceso restringido
dc.subjectTrudinger-Moser inequality
dc.subjectBlowing-up solutions
dc.subjectSingular perturbations
dc.subjectELLIPTIC-EQUATIONS
dc.subjectSINGULAR LIMITS
dc.subjectCOMPACTNESS
dc.titleNew solutions for Trudinger-Moser critical equations in R-2
dc.typeartículo


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