THE BREZIS-NIRENBERG PROBLEM ON NON-CONTRACTIBLE BOUNDED DOMAINS OF R3

Mohammed Aldawood; Cheikh Birahim Ndiaye

doi:10.3934/dcds.2025007

THE BREZIS-NIRENBERG PROBLEM ON NON-CONTRACTIBLE BOUNDED DOMAINS OF R³

Mohammed Aldawood, Cheikh Birahim Ndiaye

Howard University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we study the Brezis-Nirenberg problem on bounded smooth domains of R³. Using the algebraic topological argument of Bahri-Coron[3] as implemented in [9] combined with the Brendle[5]-Schoen[14]’s bubble construction, we solve the problem for non-contractible bounded smooth domains.

Original language	English
Pages (from-to)	2916-2948
Number of pages	33
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	45
Issue number	9
DOIs	https://doi.org/10.3934/dcds.2025007
State	Published - Sep 2025
Externally published	Yes

Keywords

Barycenter technique
homology group
inter-action estimate
PS-sequences
self-action estimate

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abstract = "In this paper, we study the Brezis-Nirenberg problem on bounded smooth domains of R3. Using the algebraic topological argument of Bahri-Coron[3] as implemented in [9] combined with the Brendle[5]-Schoen[14]{\textquoteright}s bubble construction, we solve the problem for non-contractible bounded smooth domains.",

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KW - inter-action estimate

KW - PS-sequences

KW - self-action estimate

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THE BREZIS-NIRENBERG PROBLEM ON NON-CONTRACTIBLE BOUNDED DOMAINS OF R³

Abstract

Keywords

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