On the 3-D Brezis–Nirenberg problem with small parameter
Abstract
In 2023, H. Brezis [Some of my favorite open problems, Rend. Lincei 34(2) (2023) 307–335] published a list of his “favorite open problems”, which he described as challenges he had “raised throughout his career and has resisted so far”. In this paper, we shall provide a partial answer to this question by presenting the existence of sign-changing solutions to the equation whenever the parameter is small enough. Our construction is based on the building blocks of Del Pino–Musso–Pacard–Pistoia sign-changing solutions to Yamabe problem.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Navier-Stokes equation solutions
Publication details
- Journal / source
- Communications in Contemporary Mathematics
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 28
- Issue
- 05
- Publication date
- 6 February 2026
- Language
- EN