Elliptic Equations Associated with Brownian Motion with Singular Drift

Abstract

In this paper, we first obtain the existence and uniqueness of solution u of elliptic equation associated with Brownian motion with singular drift. We then use the regularity of the weak solution u and the Zvonkin-type transformation to show that there is a unique weak solution to a stochastic differential equation when the drift is a measurable function.

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Acknowledgements

We thank the referees for their valuable comments which helped to considerably improve the quality of the paper. This work is partly supported by National Natural Science Foundation of China (No.11671372, No.11721101, No.11971456) and the Fundamental Research Funds for the Central Universities, China (No. WK0010000057).

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Correspondence to Saisai Yang.

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Yang, S., Wang, C. & Zhang, T. Elliptic Equations Associated with Brownian Motion with Singular Drift. Commun. Math. Stat. (2021). https://doi.org/10.1007/s40304-020-00213-8

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Keywords

  • Elliptic equations
  • Zvonkin-type transformation
  • Weak solution
  • Singular drift

Mathematics Subject Classification

  • 60H30
  • 60H1
  • 35J15