English

$C^{\alpha}$ regularity of weak solutions of non-homogenous ultraparabolic equations with drift terms

Analysis of PDEs 2019-06-04 v2

Abstract

Consider a class of non-homogenous ultraparabolic differential equations with drift terms or lower order terms arising from some physical models, and we prove that weak solutions are H\"{o}lder continuous, which also generalizes the classic results of parabolic equations of second order. The main ingredients are a type of weak Poincar\'{e} inequality satisfied by non-negative weak sub-solutions and Moser iteration.

Keywords

Cite

@article{arxiv.1704.05323,
  title  = {$C^{\alpha}$ regularity of weak solutions of non-homogenous ultraparabolic equations with drift terms},
  author = {Wendong Wang and Liqun Zhang},
  journal= {arXiv preprint arXiv:1704.05323},
  year   = {2019}
}

Comments

We delete the Prandtl part and add some details for $L^\infty$ estimate. arXiv admin note: text overlap with arXiv:0711.3411