$C^{\alpha}$ 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