Continuous maximal regularity on uniformly regular Riemannian manifolds
Analysis of PDEs
2016-09-29 v1 Differential Geometry
Abstract
We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize and become real analytic in space and time. The regularity result is obtained by introducing a family of parameter-dependent diffeomorphims acting on functions over Riemannian manifolds in conjunction with maximal regularity and the implicit function theorem.
Cite
@article{arxiv.1309.2041,
title = {Continuous maximal regularity on uniformly regular Riemannian manifolds},
author = {Yuanzhen Shao and Gieri Simonett},
journal= {arXiv preprint arXiv:1309.2041},
year = {2016}
}