C^(α)regularity of weak solutions of non-homogeneous ultraparabolic equations with drift terms  

作　　者：Wendong Wang Liqun Zhang 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China [2]Institute of Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Science China Mathematics》2024年第1期23-44,共22页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.12071054);National Support Program for Young Top-Notch Talents;Dalian High-Level Talent Innovation Project(Grant No.2020RD09);supported by National Natural Science Foundation of China(Grant Nos.11471320,11631008 and 12031012)。

摘　　要：We consider a class of non-homogeneous ultraparabolic differential equations with singular drift terms arising from some physical models,and prove that weak solutions are H?lder continuous,which are sharp in some sense and also generalize the well-known De Giorgi-Nash-Moser theory to degenerate parabolic equations satisfying the H?rmander hypoellipticity condition.The new ingredients are manifested in two aspects:on the one hand,for lower-order terms,we exploit a new Sobolev inequality suitable for the Moser iteration by improving the result of Pascucci and Polidoro(2004);on the other hand,we explore the G-function from an early idea of Kruzhkov(1964)and an approximate weak Poincaréinequality for non-negative weak sub-solutions to prove the H?lder regularity.

关 键 词：ultraparabolic equations Moser iteration Poincare inequality C^a regularity 

分 类 号：O175.26[理学—数学]