Corrigendum to “Fine multibubble analysis in the higher-dimensional Brezis–Nirenberg problem”

Abstract

In this corrigendum, we correct an inaccuracy in the proofs of Propositions 2.5 and 2.6 in Ann. Inst. H. Poincaré C Anal. Non Linéaire 41, 1239–1287 (2024). Indeed, to obtain the refined error terms $q_{i,\epsilon }$ and $p_{i,\epsilon }$ we subtract only a radial term in Ann. Inst. H. Poincaré C Anal. Non Linéaire 41, 1239–1287 (2024), but in fact to ensure the desired properties of $q_{i,\epsilon }$ and $p_{i,\epsilon }$ one needs to subtract the whole Hessian. This change does not affect the main result of Ann. Inst. H. Poincaré C Anal. Non Linéaire 41, 1239–1287 (2024), Theorem 1.1, up to the expression of the refined local asymptotics which must include all second derivatives. Moreover, the mentioned refinement can be accommodated in a natural way into the existing proofs of Proposition 2.5 and 2.6 given in Ann. Inst. H. Poincaré C Anal. Non Linéaire 41, 1239–1287 (2024).

Link to the paper corrected hereby.