JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (6): 46-56.doi: 10.6040/j.issn.1671-9352.0.2022.520

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Global BMO estimations for obstacle problems of a class of non-uniformly elliptic equations

Yanmin GUO(),Song ZHAO,Yuxia TONG*()   

  1. College of Science, North China University of Science and Technology, Tangshan 063210, Hebei, China
  • Received:2022-10-07 Online:2023-06-20 Published:2023-05-23
  • Contact: Yuxia TONG E-mail:guoyanmin1125@126.com;tongyuxia@126.com

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Abstract:

The regularity of weak solutions to the obstacle problem for non-uniformly elliptic equations is studied. When the gradient of the solution to the asymptotic regular problem is close to infinity, the solution of the regular problem is used to obtain an approximate solution to the asymptotic regular problem, and the bounded mean oscillation (BMO) estimates of the weak solutions gradient of the obstacle problem are obtained based on the Young inequality and perturbation discussion.

Key words: non-uniformly elliptic equation, obstacle problem, weak solution, global BMO estimation

CLC Number: 

  • O175.25
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