The Brezis-Nirenberg problem on non-contractible bounded domains of R^3
Mohammed Aldawood, Cheikh Birahim Ndiaye
TL;DR
This paper addresses the Brezis-Nirenberg problem on non-contractible bounded domains in R^3, employing algebraic topological methods and bubble constructions to establish solutions in these complex geometries.
Contribution
It introduces a novel combination of topological and bubble techniques to solve the Brezis-Nirenberg problem on non-contractible domains.
Findings
Established existence of solutions on non-contractible domains
Extended previous methods to more complex topologies
Demonstrated the effectiveness of algebraic topological arguments in PDE problems
Abstract
In this paper, we study the Brezis-Nirenberg problem on bounded smooth domains of R3. Using the algebraic topological argument of Bahri-Coron[2] as implemented in [6] combined with the Brendle[4]- Schoen[8]'s bubble construction, we solve the problem for non-contractible domains.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Mathematical Dynamics and Fractals