Coron's problem for the critical Lane-Emden system
- Authors
- Jin, Sangdon; Kim, Seunghyeok
- Issue Date
- Oct-2023
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Critical Lane-Emden system; Coron' s problem; Blowing-up solution; Asymptotic profile
- Citation
- JOURNAL OF FUNCTIONAL ANALYSIS, v.285, no.8, pp.1 - 52
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF FUNCTIONAL ANALYSIS
- Volume
- 285
- Number
- 8
- Start Page
- 1
- End Page
- 52
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/191277
- DOI
- 10.1016/j.jfa.2023.110077
- ISSN
- 0022-1236
- Abstract
- We address the solvability of the critical Lane-Emden system in a smooth bounded domain with a small spherical hole of radius ϵ>0. We prove that the system admits a family of positive solutions that concentrate around the center of the hole as ϵ→0, obtaining a concrete qualitative description of the solutions as well. To the best of our knowledge, this is the first existence result for the critical Lane-Emden system on a bounded domain, while the non-existence result on star-shaped bounded domains has been known since the early 1990s due to Mitidieri (1993) [30] and van der Vorst (1992) [36].
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