The Cauchy problem for fully nonlinear parabolic systems on manifolds
Differential Geometry
2015-07-21 v6 Analysis of PDEs
Abstract
We show the short time existence and uniqueness of solutions to the Cauchy problem for fully nonlinear systems of arbitrary even order on closed manifolds which are strongly parabolic at the initial values. The proof uses a linearization procedure and a fixed-point argument, and the key ingredient is the well known Schauder estimates for linear, strongly parabolic systems.
Cite
@article{arxiv.1506.05030,
title = {The Cauchy problem for fully nonlinear parabolic systems on manifolds},
author = {Hong Huang},
journal= {arXiv preprint arXiv:1506.05030},
year = {2015}
}
Comments
18 pages, uniqueness added, exposition improved, a new section on linear parabolic Schauder theory added