Linear and fully nonlinear elliptic equations with Ld -drift

Nicolai V. Krylov

Research output: Contribution to journalArticlepeer-review


In subdomains of (Formula presented.) we consider uniformly elliptic equations (Formula presented.) with the growth of H with respect to (Formula presented.) controlled by the product of a function from Ld and (Formula presented.) The dependence of H on x is assumed to be of BMO type. Among other things we prove that there exists (Formula presented.) such that for any (Formula presented.) the equation with prescribed continuous boundary data has a solution in class (Formula presented.) Our results are new even if H is linear.

Original languageEnglish (US)
Pages (from-to)1778-1798
Number of pages21
JournalCommunications in Partial Differential Equations
Issue number12
StatePublished - Aug 14 2020

Bibliographical note

Funding Information:
The author is very grateful to Hongjie Dong, A. I. Nazarov, and M. Safonov, who read the first draft of the paper and pointed out several glitches in it. The referee?s comments were very helpful in what concerns the references, the author brings his many thanks to him for that.


  • Fully nonlinear equations
  • interior estimates
  • solvability
  • unbounded coefficients


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