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

Wendong Wang; Liqun Zhang

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arXiv · 1704.05323

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

Wendong Wang·Liqun Zhang

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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.

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Wendong Wang, Liqun Zhang. 2017-04-18. $C^{\alpha}$ regularity of weak solutions of non-homogenous ultraparabolic equations with drift terms. https://arxiv.org/abs/1704.05323

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