抛物型方程的小扰动解
偏微分方程分析
2012-06-01 v3
摘要
设 φ 是抛物型方程 F(D^2u, Du, u, x, t) - u_t = 0 的一个光滑解。假设 F 仅在 (D^2φ, Dφ, φ, x, t) 的一个邻域内是一致椭圆的，我们证明，由 φ 的小 L1-扰动得到的任何解保持光滑。
引用
@article{arxiv.1111.5888,
title = {Small Perturbation Solutions for Parabolic Equations},
author = {Yu Wang},
journal= {arXiv preprint arXiv:1111.5888},
year = {2012}
}
备注
This is the version to appear in Indiana Univ. Math. J. We have corrected few typos and errors that occur in earlier versions. We have also rewritten the statement of Lem.2.2 and detailed the proof of Lem 2.2-2.4