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Cα regularity of weak solutions of non-homogeneous ultraparabolic equations with drift terms

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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 Hölder continuous,which are sharp in some sense and also generalize the well-known De Giorgi-Nash-Moser theory to degenerate parabolic equations satisfying the Hörmander 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 Poincaré inequality for non-negative weak sub-solutions to prove the Hölder regularity.

ultraparabolic equationsMoser iterationPoincaré inequalityCα regularity

Wendong Wang、Liqun Zhang

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School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China

Institute of Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

National Natural Science Foundation of ChinaNational Support Program for Young Top-Notch Talents and Dalian High-Level Talent Innovation ProjectNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of China

120710542020RD09114713201163100812031012

2024

10.1007/s11425-021-2098-0

中国科学:数学(英文版)
中国科学院

中国科学:数学(英文版)

CSTPCD
影响因子：0.36
ISSN：1674-7283
年,卷(期)：2024.67(1)
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