Small Perturbation Solutions for Parabolic Equations

Yu Wang

Small Perturbation Solutions for Parabolic Equations

Analysis of PDEs 2012-06-01 v3

Authors: Yu Wang

Abstract

Let $\phi$ be a smooth solution of the parabolic equation $F(D^2u, Du, u, x, t)- u_{t} = 0$ : Assume $F$ is uniform elliptic only in a neighborhood of $(D^2\phi, D\phi, \phi, x, t)$ , we prove that any solution obtained from small L1-perturbation of $\phi$ remains smooth.

Keywords

parabolic equations

Cite

@article{arxiv.1111.5888,
  title  = {Small Perturbation Solutions for Parabolic Equations},
  author = {Yu Wang},
  journal= {arXiv preprint arXiv:1111.5888},
  year   = {2012}
}

Comments

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

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