Higher-order time asymptotics of fast diffusion in Euclidean space: A dynamical systems approach

Abstract

Introduction Overview of obstructions and strategies, and notation The nonlinear and linear equations in cigar coordinates The cigar as a Riemannian manifold Uniform manifolds and Holder spaces Schauder estimates for the heat equation Quantitative global well-posedness of the linear and nonlinear equations in Holder spaces The spectrum of the linearized equation Proof of Theorem 1.1 Asymptotic estimates in weighted spaces: The case $m \frac{n}{n+2}$. Proof of Theorem 1.2 and its corollaries Appendix A. Pedestrian derivation of all Schauder estimates Bibliography