A Priori Estimates for Finite-Energy Sign-Changing Blowing-Up Solutions of Critical Elliptic Equations
Bruno Premoselli
Abstract
Abstract We prove sharp pointwise blow-up estimates for finite-energy sign-changing solutions of critical equations of Schrödinger–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 Schrödinger–Yamabe-type equations. To deal with the sign-changing case, we develop a method of proof that combines an a priori bubble-tree analysis with a finite-dimensional reduction, and reduces the proof to obtaining sharp a priori blow-up estimates for a linear problem.
Topics & Concepts
MathematicsPointwiseA priori and a posterioriSign (mathematics)Blowing upType (biology)Dimension (graph theory)Mathematical analysisEnergy (signal processing)Elliptic curveRiemannian manifoldManifold (fluid mechanics)Applied mathematicsPure mathematicsPhilosophyMechanical engineeringEcologyStatisticsEngineeringEpistemologyBiologyNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems