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Multipeak solutions to the Bahri-Coron problem in domains with a shrinking hole |
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| Authors: | Mónica Clapp Angela Pistoia |
| Institution: | a Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510 México DF, Mexico b Departamento de Matemática, Pontificia Universidad Católica de Chile, Avenida Vicuna Mackenna 4860, Macul, Santiago, Chile c Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy d Dipartimento di Metodi e Modelli Matematici, Università di Roma “La Sapienza”, via A. Scarpa 16, 00161 Roma, Italy |
| Abstract: | We construct positive and sign changing multipeak solutions to the pure critical exponent problem in a bounded domain with a shrinking hole, having a peak which concentrates at some point inside the shrinking hole (i.e. outside the domain) and one or more peaks which concentrate at interior points of the domain. These are, to our knowledge, the first multipeak solutions in a domain with a single small hole. |
| Keywords: | Nonlinear elliptic boundary value problem Pure critical exponent Multipeak solutions |
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