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arXiv · 2111.02470

A priori estimates for finite-energy sign-changing blowing-up solutions of critical elliptic equations

Bruno Premoselli
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Abstract

We prove sharp pointwise blow-up estimates for finite-energy sign-changing solutions of critical equations of Schr\"odinger-Yamabe type on a closed Riemannian manifold $(M,g)$ of dimension $n \ge 3$. This is a generalisation of the so-called $C^0$-theory for positive solutions of Schr\"odinger-Yamabe type equations. To deal with the sign-changing case we develop a method of proof that combines an \emph{a priori} bubble-tree analysis with a finite-dimensional reduction, and reduces the proof to obtaining sharp \emph{a priori} blow-up estimates for a linear problem.

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Bruno Premoselli. 2021-11-03. A priori estimates for finite-energy sign-changing blowing-up solutions of critical elliptic equations. https://arxiv.org/abs/2111.02470

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