Multipeak solutions to the Bahri-Coron problem in domains with a shrinking hole
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
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. (C) 2008 Elsevier Inc. All rights reserved.
Description
Keywords
Nonlinear elliptic boundary value problem, Pure critical exponent, Multipeak solutions, CRITICAL SOBOLEV EXPONENT, ELLIPTIC-EQUATIONS, TOPOLOGY, GROWTH, POINT