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On Brezis' First Open Problem: A Complete Solution

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arxiv 2503.06904 v1 pith:J2266UAG submitted 2025-03-10 math.AP math.DG

Liming Sun , Juncheng Wei , Wen Yang This is my paper · ORCID
classification math.APmath.DG
keywords problembrezisopensolutionscompleteexistencefavoritefirst
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In 2023, H.\,Brezis published a list of his ``favorite open problems", which he described as challenges he had ``raised throughout his career and has resisted so far". We provide a complete resolution to the first one--Open Problem 1.1--in Brezis's favorite open problems list: the existence of solutions to the long-standing Brezis-Nirenberg problem on a three-dimensional ball. Furthermore, using the building blocks of Del Pino-Musso-Pacard-Pistoia sign-changing solutions to the Yamabe problem, we establish the existence of infinitely many sign-changing, nonradial solutions for the full range of the parameter.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A refined blow-up analysis of the Brezis-Nirenberg equation and its application: The one-bubble case for $N\geq4$

    math.AP 2026-07 accept novelty 7.0 of 10

    Refined inverse-reduction blow-up analysis classifies one-bubble Struwe decompositions of the Brezis-Nirenberg equation for N≥4 and proves least-energy sign-changing solutions exist at every eigenvalue in 4D.

  2. Sharp quantitative stability estimates for the Brezis-Nirenberg problem

    math.AP 2025-06 conditional novelty 7.0 of 10

    Nearly stationary functions for the Brezis-Nirenberg problem on bounded domains lie within a sharp, dimension-dependent distance of a solution plus bubbles, and the optimal exponents are identified.

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