Fine multibubble analysis in the higher-dimensional Brezis–Nirenberg problem

  • Tobias König

    Goethe-Universität Frankfurt, Frankfurt am Main, Germany
  • Paul Laurain

    Institut de Mathématiques de Jussieu, Paris, France; École Normale Supérieure - PSL, Paris, France
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Abstract

For a bounded set and a perturbation , we analyze the concentration behavior of a blow-up sequence of positive solutions to for dimensions , which are non-critical in the sense of the Brezis–Nirenberg problem. For the general case of multiple concentration points, we prove that concentration points are isolated and characterize the vector of these points as a critical point of a suitable function derived from the Green function of on . Moreover, we give the leading-order expression of the concentration speed. This paper, with a recent one by the authors [arXiv:2208.12337, 2022] in dimension , gives a complete picture of blow-up phenomena in the Brezis–Nirenberg framework.

Cite this article

Tobias König, Paul Laurain, Fine multibubble analysis in the higher-dimensional Brezis–Nirenberg problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 41 (2024), no. 5, pp. 1239–1287

DOI 10.4171/AIHPC/95