Potential Theory on Minimal Hypersurfaces II: Hardy Structures and\n Schr "odinger Operators

2018/10/07 by Joachim Lohkamp, Lohkamp, Joachim
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Harmonic Analysis Research #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1810.03154

Abstract

We extend the potential theory on almost minimzers from Part 1. We introduce\nso-called Hardy structures to study many classical operators using the tools\nfrom part 1. Furthermore, we show that for a naturally defined operator L,\nminimal growth of positive solutions of Lw = 0 towards the singular set is a\nstable property. It persists under perturbations or blow-ups of the underlying\nspaces. This is the key result to develop a dimensional induction scheme for\nthe asymptotic analysis of these operators near the singular set.\n

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