An analytic construction of singular solutions related to a critical Yamabe problem
Metadata only
Date
2020Type
- Journal Article
Abstract
We answer affirmatively a question posed by Aviles in 1983, concerning the construction of singular solutions of semilinear equations without using phase-plane analysis. Fully exploiting the semilinearity and the stability of the linearized operator in any dimension, our techniques involve a careful gluing in weighted (Formula presented.) spaces that handles multiple occurrences of criticality, without the need of derivative estimates. The above solution constitutes an Ansatz for the Yamabe problem with a prescribed singular set of maximal dimension (Formula presented.) for which, using the same machinery, we provide an alternative construction to the one given by Pacard. His linear theory uses Lp-theory on manifolds, while our strategy relies solely on asymptotic analysis and is suitable for generalization to non-local problems. Indeed, in a forthcoming paper, we will prove analogous results in the fractional setting. © 2020 Taylor & Francis Group, LLC. Show more
Publication status
publishedExternal links
Journal / series
Communications in Partial Differential EquationsVolume
Pages / Article No.
Publisher
Taylor & FrancisSubject
Critical Yamabe problem; Gluing construction; Higher dimensional singularity; Lane-Emden equation; Singular solution; Stable solutionFunding
721675 - Regularity and Stability in Partial Differential Equations (EC)
More
Show all metadata